DUFFLY, J.

After a mistrial at which the jury were deadlocked, the defendant was retried and convicted of two indictments charging murder in the first degree on a theory of deliberate premeditation.1 On appeal, the defendant claims that his motion to dismiss the indictments, filed before retrial, should have been allowed because the Commonwealth had not presented legally sufficient evidence at his first trial; a second trial in these circumstances, he contends, violated constitutional and common-law prohibitions against double jeopardy. The defendant argues further that the Commonwealth's evidence at the second trial was legally insufficient to support the convictions, and that his motions for required findings of not guilty therefore should have been allowed. Additionally, the defendant challenges various evidentiary rulings, claims that the judge erred in failing to instruct the jury pursuant to Commonwealth v. Bowden, 379 Mass. 472, 485-486 (1980) (permitting defense theory of inadequate police investigation), and contends that other errors at trial warrant reversal of his convictions under G. L. c. 278, § 33E. After reviewing the entire record, we affirm the convictions and decline to grant relief pursuant to G. L. c. 278, § 33E.

1. Background. Because the defendant challenges the sufficiency of the evidence, we recite the facts the jury could have found in the light most favorable to the Commonwealth, see Commonwealth v. Latimore, 378 Mass. 671, 676-677 (1979), reserving certain details for our discussion of the specific issues raised.2

Just before 8 A.M. on Monday, March 13, 2006, Michael Zammitti, Sr., arrived at Allstate Concrete Pumping, Inc. (Allstate), on New Salem Street in Wakefield. He owned and operated the business with his son, Michael Jr.3 As Michael Sr. entered the building, he discovered the body of Chester Roberts, Jr., one of his employees, on the floor in a pool of blood. Michael Sr. telephoned police and rushed upstairs to look for Michael Jr.; he found his son with an apparent gunshot wound to the head, seated at his desk in an upstairs office. Each victim had died as a result of a sixteen-gauge shotgun wound4 inflicted only minutes before Michael Sr. arrived.5

In the early hours of their investigation, police received numerous potential leads. Bystanders described seeing at least two suspicious vehicles in the area of New Salem Street that morning, and Michael Sr. provided police with several names of people with whom he had had contentious business dealings. Police quickly determined that many of these leads were not viable, and focused their investigation on the defendant, who had been romantically involved with Michael Jr.'s wife, Michele.

Beginning in 2004, the defendant and Michele developed what was initially a close friendship. The defendant was a year-round resident of a small community of predominately seasonal homes in Freedom, New Hampshire. Michael Sr. and his wife, Patricia, had owned a vacation home there for many years; Michael Jr. and Michele had recently purchased a vacation home in that area as well. Because Michael Jr. worked long hours in Wakefield, Michele and the couple's three young children often traveled to Freedom without him. The defendant, whose relationship with a live-in girl friend had ended some years before, became friendly with Michele and her children, and the group often participated in recreational activities together. When Michele was away from her New Hampshire home, she and the defendant talked frequently by telephone. In January, 2005, the defendant told Michele that he had fallen in love with her; shortly thereafter, they became sexually intimate.

During the summer of 2005, Michele and Michael Jr. recognized that their relationship had become strained and began to participate in marriage counselling; Michele became increasingly committed to repairing her marriage. In August, 2005, Michele's mother-in-law discovered Michele and the defendant in an "embrace." After discussing the incident with her mother-in-law, Michele began to distance herself from the defendant, although she attempted to remain on cordial terms with him for the sake of the children, who had grown fond of him, and in order to deflect the suspicions of her in-laws and neighbors. The defendant continued to urge Michele to leave her husband; in December, 2005, Michele informed the defendant that she wanted to end the relationship.

A few weeks before the shootings, Michele acquiesced to the defendant's requests that they meet in February, when she and the children would be on vacation in New Hampshire. The defendant had prepared for a romantic interlude and, during the meeting, again tried to persuade Michele to leave her husband. Michele made clear that she would not leave her husband, stating that the only way she and the defendant could be together would be if her husband left her or if "something happened to him." The defendant became angry; he pounded his fist on the table and shoved Michele into her automobile, slamming the door shut. In the weeks leading up to the murders, the defendant continued to press Michele to leave her husband; he told his best friend, David Spears, whose father also owned a home in Freedom, that a job offer he had recently received was not enough to support a family of five and that he was trying to figure out a way to salvage his relationship with Michele.

After learning about Michele's relationship with the defendant, police suspected that the defendant might have been responsible for the shootings, but initially had no evidence connecting him to the scene of the shootings. On March 29, 2006, Detective Richard F. Cass of the Wakefield police department, accompanied by State police Trooper Kevin Baker, traveled to Freedom to "look into" a series of suspicious housebreaks because they were "of interest." Two houses were of particular interest to Cass: the home of Michael Sr., from which a sixteen-gauge shotgun was discovered to be missing, and the summer home of Fred Martin, who lived across the street from Michael Sr. and next door to the defendant.

When Cass looked at Martin's property, he saw a green Ford F150 pickup truck with an extended cab parked outside. The vehicle was similar to a green truck Cass had observed in surveillance footage recorded by the cameras of three businesses on New Salem Street on the morning of the shootings. Baker contacted Martin at his seasonal home in Florida and obtained permission to take possession of the truck.6 Following his conversation with Baker, Martin used the Internet to check for activity on his "E-ZPass" account.7 Although Martin had been in Florida for several months, his account showed that a single transaction had occurred in a northbound lane at New Hampshire's Dover toll plaza on the morning of March 13, 2006.

Martin executed a written waiver of any privilege or right of confidentiality he might have had in his E-ZPass records, which enabled police to obtain toll data for March 13 from the New Hampshire Department of Transportation. The data revealed that, on the morning of the shootings, Martin's E-ZPass had traveled southbound in New Hampshire through toll plazas in Rochester at 6:40 A.M., Dover at 6:51 A.M., and through the Hampton toll plaza at 7:04 A.M. At each toll plaza, however, the driver of the vehicle paid cash, and the electronic transaction was canceled.8 Martin's transponder also was recorded traveling northbound through the same three toll plazas later on the morning of March 13: Hampton at 8:29 A.M., Dover at 8:41 A.M., and Rochester at 8:51 A.M. The driver again paid cash at each northbound toll plaza, but an attendant at the northbound Dover toll plaza inadvertently failed to cancel the transaction, creating the entry Martin later discovered on his account statement.

After receiving this information, State police Trooper Robert Manning drove from Freedom to Wakefield to determine whether the activity on Martin's E-ZPass was consistent with someone arriving at Allstate just before 8 A.M. Manning testified that he left Freedom at 5:44 A.M. and arrived at Allstate just over two hours later, at 7:54 A.M.9 Manning's toll receipts from that trip reflect that he drove southbound through the toll plazas in Rochester at 6:48 A.M., Dover at 6:57 A.M., and Hampton at 7:14 A.M.

Detectives also reviewed surveillance footage from cameras at businesses located along New Salem Street to determine whether this timing was consistent with the presence of the green pickup truck with an extended cab that was recorded traveling down New Salem Street on the morning of the shootings. The footage first shows the green truck traveling along New Salem Street at approximately 7:38 A.M.,10 when it appears to continue past Allstate without stopping. Approximately one minute later, a white pickup truck resembling the one driven by Michael Jr. appears on New Salem Street and enters the Allstate parking lot. At approximately 7:44 A.M., the green truck appears again as it travels down New Salem Street a second time and enters the Allstate parking lot.11 In the footage, a pedestrian walks from the area of a neighboring business toward Allstate about one minute later.12 At 7:48 A.M., the green truck can be seen leaving the Allstate parking lot and driving northbound along New Salem Street.13 A red pickup truck resembling the one driven by Michael Sr. enters the Allstate parking lot at approximately 8:02 A.M.

Although Martin had never authorized the defendant to be in his truck and had never seen the defendant in his truck, deoxyribonucleic acid (DNA) recovered from the vehicle's steering wheel contained a mixture of DNA from at least two people, with the major profile being a match for the defendant's DNA.14 The defendant was also included as a potential contributor to the minor profile of a mixture of DNA that was found on a key to the truck that was inside the vehicle when police took possession of it.15,16 Additionally, in the truck's bed, police recovered an uncoiled wire coat hanger that had been bent in such a way that it could be used to unlock the door of an automobile without keys.17 DNA testing of the coat hanger yielded inconclusive results for comparison to the defendant.

Police also interviewed the defendant's neighbors in Freedom to determine if anyone had seen the defendant on the morning of the shootings. Gertrude Ducharme, who lived across the street from the defendant, told police that she saw the defendant just after 10 A.M. on the morning of March 13, as she was leaving her house to start her daily walk. The defendant had been leaning against his truck, parked in his driveway, and called out to Ducharme as she walked past him; he later sent Ducharme a letter that stated, "And you, Gert, stay healthy. You are the only one who saw me that morning."

The defendant told police that he had first learned of the shootings when he spoke to his friend, Paul Taylor, on the telephone at approximately 9 A.M. on March 13, but the defendant's telephone records showed that the call had not occurred until 10:34 A.M. The defendant told police that he immediately went to Ducharme's house to tell her about the murders, but that Ducharme had already learned of the murders during a telephone call with Michele. Ducharme testified that she had never spoken to Michele on the telephone — on that morning or any other — and that the defendant did not come over to her house until sometime later in the day; when he did, the defendant announced, "Mike's been shot. It was a hit."18

The defendant's telephone records also showed that he had spoken to Spears at 12:29 P.M. In that conversation, the defendant revealed details of the crime that had not yet been established. The defendant informed Spears that Michael Jr. had been killed at 8 A.M.; although police had received a 911 call from Michael Sr. at approximately 8 A.M., at that point they had not yet established the time of death. The defendant attempted to establish that he had learned about the time of the shootings when speaking to Taylor, but Taylor testified that he neither knew nor said anything to the defendant about the time of the shootings.

2. Sufficiency of the evidence. a. Motion to dismiss. The jury at the defendant's first trial were deadlocked, and the judge declared a mistrial. Before retrial, the defendant moved to dismiss the case on the ground that the Commonwealth had failed to present legally sufficient evidence to support the convictions. The defendant contends that, by denying his motion and subjecting him to a second trial, the judge19 violated his constitutional and common-law protections against double jeopardy.

"Under the double jeopardy clause of the Fifth Amendment, applicable to the States through the Fourteenth Amendment to the United States Constitution, and Massachusetts statutory and common law, no person may be twice placed in jeopardy for the same criminal offense." Cruz v. Commonwealth, 461 Mass. 664, 670 (2012). "Consequently, once jeopardy has attached, a judge may declare a mistrial over a defendant's objection and commence a new trial only in light of a `manifest necessity.'" Id., quoting Commonwealth v. Nicoll, 452 Mass. 816, 818 (2008). "The `prototypical example' of a manifest necessity for a judge to declare a mistrial is a deadlocked jury." Commonwealth v. Ellis, 432 Mass. 746, 751 (2000), quoting Commonwealth v. Andrews, 403 Mass. 441, 448-449 (1988). As the defendant correctly observes, however, double jeopardy does not permit retrial where the evidence presented by the Commonwealth at the defendant's first trial was legally insufficient to convict. See Corson v. Commonwealth, 428 Mass. 193, 196 (1998); Berry v. Commonwealth, 393 Mass. 793, 794 (1985).

In reviewing the defendant's motion to dismiss based on the sufficiency of the evidence at the first trial, we apply the same standard that we use to consider the defendant's motion for required findings of not guilty based on the sufficiency of the evidence at the second trial. In both instances, we consider "whether the evidence produced by the Commonwealth in its case-in-chief was sufficient to convict on the crimes charged." Commonwealth v. Jansen, 459 Mass. 21, 27 (2011). "The evidence may be primarily or entirely circumstantial, provided that, when viewed in the light most favorable to the Commonwealth, it `and the inferences permitted to be drawn therefrom [are] of sufficient force to bring minds of ordinary intelligence and sagacity to the persuasion of [guilt] beyond a reasonable doubt.'" Id., quoting Commonwealth v. Latimore, 378 Mass. 671, 677 (1979).

The defendant acknowledges that the Commonwealth's evidence at each trial was substantially the same.20 The thrust of his challenge to the sufficiency of the evidence in both trials is that there was no direct evidence connecting him to the shootings. There were no eyewitnesses and no forensic evidence that connected him to the scene, and the only evidence connecting him to Martin's truck was a degraded DNA sample. Without more, the defendant contends, the Commonwealth's evidence was insufficient to prove the charges beyond a reasonable doubt. We disagree.

A conviction may be based primarily or exclusively on circumstantial evidence and the permissible inferences that may be drawn therefrom. Corson v. Commonwealth, supra at 197. To be permissible, an inference need only be "reasonable and possible," not "necessary or inescapable." Commonwealth v. Casale, 381 Mass. 167, 173 (1980). "Whether an inference is warranted or is impermissibly remote must be determined, not by hard and fast rules of law, but by experience and common sense." Commonwealth v. Lao, 443 Mass. 770, 779 (2005), S.C., 450 Mass. 215 (2007), and 460 Mass. 12 (2011), quoting Commonwealth v. Giang, 402 Mass. 604, 609 (1988). "If, from the evidence, conflicting inferences are possible, it is for the jury to determine where the truth lies, for the weight and credibility of the evidence is wholly within their province." Commonwealth v. Lao, supra.

Viewed in the light most favorable to the Commonwealth, see Commonwealth v. Latimore, supra, the evidence presented at the defendant's first trial was sufficient to establish that he committed the murders with deliberate premeditation. There was evidence that the defendant had a motive to kill Michael Jr. He had been engaged in an affair with Michele, who, shortly before the shootings, sought to end the relationship and told the defendant that the only way they could be together was if "something happened" to her husband. See Commonwealth v. Linton, 456 Mass. 534, 545 (2010) (defendant had motive to prevent victim from interfering with adulterous sexual relationship); Commonwealth v. Lao, supra at 780 (defendant had motive to kill estranged wife who had started relationship with another man). The evidence also permitted an inference that the defendant had a motive to kill Roberts, who happened to arrive at Allstate while the defendant was present and could have identified the defendant as Michael Jr.'s killer. See Commonwealth v. Barbosa, 457 Mass. 773, 794 (2010), cert. denied, 131 S.Ct. 2441 (2011).

The evidence also established that the defendant had the opportunity to commit the crimes. According to State police Sergeant Richard Mahoney's testimony, the drive between the Allstate building in Wakefield and the defendant's residence in Freedom took approximately two hours. Despite the defendant's efforts to establish his presence in Freedom on the morning of March 13, 2006, no one saw him there until after 10 A.M. — just over two hours after the murders occurred. In addition, there was testimony that the defendant had driven to Allstate's building in Wakefield in the past; Taylor testified that the defendant had been there earlier during the prior year to pick up a sander from Michael Sr. From this evidence, the jury could have inferred that the defendant was familiar with the route and timing of the drive to Wakefield, as well as the layout of the Allstate building.

The inference that the defendant was present at the Allstate building at the time of the shootings is reinforced by Martin's E-ZPass records, which recorded toll activity at times consistent with travel from the defendant's home in Freedom to Allstate in Wakefield, and which correlated directly with surveillance footage from area businesses that recorded a green truck resembling Martin's entering the Allstate parking lot. From evidence that the driver paid cash rather than use the E-ZPass, the jury could have inferred that the driver wanted to avoid having the transactions recorded. In addition, Martin testified that the defendant had never been inside the truck, yet the defendant's DNA matched the major profile of DNA found on the steering wheel and he was included as a potential contributor of the minor DNA profile found on a key to the truck. There was also testimony that the position of Martin's truck when police found it was different from how Martin had left it, supporting the inference that the defendant had rushed to park the vehicle upon his return so that he could be standing in his driveway in time to talk to Ducharme when she passed his house on her customary 10 A.M. walk.

In arguing that this evidence is insufficient, the defendant places great emphasis on our decision in Commonwealth v. Mazza, 399 Mass. 395 (1987). In that case, we concluded that the evidence of the defendant's motive and opportunity to murder the victim was insufficient "to identify the defendant as the perpetrator." Id. at 399. The evidence in that case established only that the defendant and the victim were interested in the same woman; that the defendant had telephoned the victim about one and one-half hours before the victim's body was discovered; that the defendant had been present at a restaurant parking lot about one hour before the victim's body was discovered there; and that, when the defendant returned from the parking lot after being there for one and one-half minutes, he said to a friend, "There's a problem." Id. at 396. We concluded that evidence of the defendant's motive, opportunity, and presence at the scene was insufficient where the Commonwealth had not proved that the defendant was carrying a gun on the day of the murder, or that the defendant was at the restaurant at the time the murder took place. Id. at 399. By contrast, the evidence in this case established that the fatal shots were fired shortly before 8 A.M.; based on reasonable inferences drawn from multiple sources of evidence, the jury could have concluded that the defendant had driven to Allstate in Martin's green truck, where he arrived shortly before 8 A.M.

In addition, there was significant evidence showing the defendant's consciousness of guilt, which strengthened the circumstantial evidence of the defendant's guilt. See Commonwealth v. O'Laughlin, 446 Mass. 188, 202-203 (2006) (significant evidence establishing defendant's consciousness of guilt may compensate for relatively weak circumstantial evidence).21 The jury could have found that, in order to deflect suspicion away from himself, the defendant had attempted to establish that he was in Freedom between 9 A.M. and 9:30 A.M. — a time frame that would have precluded his being in Wakefield at the time of the shootings — by parking his own red truck, which he usually parked inside his garage, in his driveway so that it would be visible. When interviewed by police after the shootings, the defendant insisted he had been in Freedom on the morning of the shootings. Although Ducharme told police that she had seen the defendant in front of his home just after 10 A.M., the defendant told police that she had seen him at 9 A.M. and later told Spears that she had seen him at 9:30 A.M. He also told Spears that he had been having coffee at a local market at the time of the shootings, but did not repeat this alibi to police after learning that the market was equipped with surveillance cameras.

The jury could have found that the defendant's statements to others, and to police, regarding his whereabouts on the morning of the shootings were wilfully false and consistent with consciousness of guilt. See Commonwealth v. Robles, 423 Mass. 62, 71 (1996), citing Commonwealth v. Bonomi, 335 Mass. 327, 348 (1957) (consciousness of guilt may be inferred from defendant's wilfully false statements). Finally, the defendant's consciousness of guilt could also have been inferred from evidence that the defendant sent an anonymous, threatening letter to Michael Sr. in an effort to make it appear as though the shootings had to do with Allstate's business. The defendant had first suggested that the shootings were business related when he told Ducharme on the afternoon of March 13 that the shooting of Michael Jr. had been "a hit."

There was considerable evidence linking the defendant to the shootings. The evidence of the defendant's motive, opportunity, and consciousness of guilt was sufficient to prove beyond a reasonable doubt that the defendant killed both victims. The judge did not err in denying the defendant's motion to dismiss.

b. Motions for required findings of not guilty.22 As noted, the evidence at the defendant's second trial was substantially identical to the evidence presented at the first trial. In addition, the second jury heard testimony from Eric Kalis, an engineer at Ford Motor Company, who offered his opinion that the green truck depicted in the surveillance footage was a Ford F150 pickup truck with an extended cab that had been manufactured between 1992 and 1996, consistent with the model owned by Martin. Although Kalis's testimony was not essential to establishing the inference that the vehicle on the surveillance tapes was in fact Martin's pickup truck, it added weight on this point. From this evidence, and the evidence described in part 2.a, supra, the defendant's motions for a required finding of not guilty were properly denied.

3. Third-party culprit evidence. The defendant contends also that the judge erred by preventing him from introducing evidence during the second trial that someone other than the defendant was responsible for the shootings. In particular, the defendant sought to cast suspicion on Ricky Cali, a former Allstate employee who had sued Michael Sr. over a labor dispute in 1995, eleven years before the shootings. The defendant argued that Cali had a motive to commit the crimes: Michael Sr. had threatened to "knock [Cali's mother's] house down with a bulldozer" during the course of their dispute. The lawsuit was eventually settled, but Cali expressed dissatisfaction with the settlement terms. The defendant argued also that Cali had had the means to commit the murders because he owned several shotguns.

The Commonwealth moved in limine to exclude any third-party culprit evidence regarding Cali. In the Commonwealth's view, the eleven-year span between Cali's dispute — which was with Michael Sr. and not either of the victims — rendered the defendant's theory too remote and speculative to be admissible. The judge agreed, stating that "[i]f there was evidence that could be produced that showed that this particular individual,... Cali, was in fact a viable suspect, I think it would be in a slightly different posture than it is now. But as I understand it, other than some animosity, significant animosity, between the families, that's the only evidence." Accordingly, the judge ruled that the defendant would not be permitted to question witnesses about the details of the hostility between Cali and Michael Sr.23

It is well established that "[a] defendant has a constitutional right to present evidence that another may have committed the crime." Commonwealth v. Conkey, 443 Mass. 60, 66 (2004), S.C., 452 Mass. 1022 (2008). A defendant may "introduce evidence that tends to show that another person committed the crime or had the motive, intent, and opportunity to commit it." Commonwealth v. Lawrence, 404 Mass. 378, 387 (1989), quoting Commonwealth v. Harris, 395 Mass. 296, 300 (1985). Although we have called the use of third-party culprit evidence "a time-honored method of defending against a criminal charge," Commonwealth v. Rosa, 422 Mass. 18, 22 (1996), we have also recognized that a defendant's right to present such evidence is subject to certain limitations. Among these is the requirement that the evidence "must have a rational tendency to prove the issue the defense raises, and the evidence cannot be too remote or speculative." Commonwealth v. Smith, 461 Mass. 438, 445-446 (2012), quoting Commonwealth v. Silva-Santiago, 453 Mass. 782, 801 (2009).

Here, the judge correctly concluded that the defendant's proffered evidence about hostility between Cali and Michael Sr. was too remote and speculative to be admissible. The only evidence arguably linking Cali to the shootings was a labor dispute that had occurred more than a decade earlier. Although the defendant proffered evidence that the families had remained distant from each other since that time, no evidence was proffered to suggest that Cali's animosity toward Michael Sr. had been rekindled after 1995, let alone that it had grown to the point that it would support a motive for murder. To the contrary, Michael Sr. testified that he and Cali had largely resolved their differences in the intervening years. There was also no evidence to suggest that Cali had the means or opportunity to commit the crime.24 Contrast Commonwealth v. Conkey, supra at 68-70 (concluding that third-party culprit evidence should have been admitted where third party had motive and opportunity to commit crime and had exhibited consciousness of guilt, and where proffered evidence demonstrated that third party had engaged in pattern of conduct consistent with details of crime). There was no error in the judge's decision to exclude this evidence.

4. Bowden defense and jury instruction. Related to the defendant's third-party culprit claim is his argument that the judge improperly limited his defense under Commonwealth v. Bowden, 379 Mass. 472, 485-486 (1980) (Bowden), and that she erred by not giving a corresponding instruction to the jury. A defendant is entitled to present evidence suggesting that police failed to conduct an adequate investigation. Id. A "Bowden defense," as it has commonly come to be known, may focus on either the failure of police to conduct certain scientific tests or their failure to investigate leads concerning suspects other than the defendant. Commonwealth v. Silva-Santiago, supra at 802.

A defendant may invoke a Bowden defense to suggest that police failed to investigate other potential suspects and a third-party culprit defense to suggest that those other suspects actually committed the crime charged. See id. at 800-801. Accordingly, it is not uncommon for evidence relevant to a third-party culprit defense to be admitted as part of a Bowden defense. However, "[i]n contrast to the third-party culprit defense, where evidence may be admitted regardless of whether the police knew of the suspect, third-party culprit information is admissible under a Bowden defense only if the police had learned of it during the investigation and failed reasonably to act on the information" (emphasis in original). Commonwealth v. Silva-Santiago, supra at 803.

The defendant's argument with respect to his Bowden defense overlooks this limitation. He contends that the trial judge repeatedly stymied his efforts to question police witnesses about their failure to follow certain leads concerning other potential suspects. The record does not support this claim. Passages in the trial transcript cited by the defendant in support of this argument exemplify the judge's consistent rulings throughout the trial that appropriately limited the Bowden evidence to information that the police knew or reasonably should have known in the course of their investigation.25 Contrary to the defendant's claim, the judge afforded defense counsel wide latitude to expose purported inadequacies in the police investigation. The defendant was permitted to question witnesses about the nature of the dispute between Michael Sr. and Cali, the steps police did and did not take to follow up on that lead, and the extent of the police investigation with respect to several other potential suspects. The judge correctly applied our case law in this area, see Commonwealth v. Silva-Santiago, supra at 803, and did not foreclose any argument that the defendant was entitled to make under Bowden.

To the extent the defendant argues that the judge should have instructed the jury regarding the adequacy of the police investigation, this argument also fails. In denying the defendant's request for a Bowden instruction at the second trial, the judge correctly stated the law when she said that such an instruction is "never required under our case law." See Commonwealth v. Williams, 439 Mass. 678, 687 (2003) (instruction on adequacy of police investigation "is never required. In other words, there is no Bowden instruction"). In Bowden, supra at 486, we held that a judge may not foreclose the jury's consideration of the adequacy of the police investigation; we did not establish an affirmative requirement that the judge instruct the jury concerning their consideration of those perceived inadequacies.26 See Commonwealth v. Boateng, 438 Mass. 498, 506-507 (2003). The judge did not prevent the defendant from questioning the adequacy of the police investigation, nor did she remove the issue from the jury's consideration. Bowden requires no more.

5. New Hampshire toll records. Before the first trial, the Commonwealth moved to admit Martin's New Hampshire E-ZPass records, which it had obtained from the New Hampshire Department of Transportation. A judge other than the trial judge (motion judge) allowed that motion. The defendant argues that it was error for the motion judge to allow the motion because New Hampshire law requires E-ZPass records remain confidential. The applicable statute provides, in relevant part:

N.H. Rev. Stat. Ann. § 237:16-e (LexisNexis 2008). The defendant suggests that the E-ZPass records admitted in this case serve to identify a vehicle (Martin's truck) and, by inference, the defendant as its occupant. He claims that he therefore has a stake in the controversy sufficient to satisfy traditional standing requirements. Even assuming that the defendant does have standing to raise this issue, a question we do not decide, we disagree that the statute bars the use of Martin's E-ZPass records "in any court in any action or proceeding," including a criminal proceeding in Massachusetts. Id.

We shall assume, as did the motion judge, that N.H. Rev. Stat. Ann. § 237:16-e, as in effect at the time of trial, creates an evidentiary privilege in E-ZPass data for account holders, and perhaps for those who use a transponder with an account holder's consent. However, under both Massachusetts and New Hampshire law, evidentiary privileges are to be narrowly construed and are generally waivable. See, e.g., Commissioner of Revenue v. Comcast Corp., 453 Mass. 293, 304 (2009); State v. Melvin, 132 N.H. 308, 309-310 (1989).

As the parties observe, there are no cases interpreting N.H. Rev. Stat. Ann. § 237:16-e or the analogous Massachusetts statute. See G. L. c. 6C, § 13 (a). Nonetheless, based on the plain language of the statute, we conclude that, however broadly the New Hampshire Legislature may have intended the privilege to reach, it has no bearing in the circumstances of this case. Martin's transponder was used on the day of the shootings without his knowledge or consent. Martin, the only person authorized to use the transponder, thereafter executed a written waiver of any privilege or right to confidentiality he may have had in his E-ZPass records. Nothing in the statute suggests that such a waiver should not be given effect. The motion judge appropriately gave effect to Martin's waiver and did not err in ruling that the E-ZPass records were admissible.

6. DNA evidence. The defendant contends that the trial judge erred in permitting the Commonwealth's DNA analyst to testify at the second trial about inconclusive test results from the wire coat hanger found in the bed of Martin's truck. He argues also that a chart depicting the results of the DNA testing of the coat hanger and various locations in Martin's truck should not have been admitted. Both claims are without merit.

Over the defendant's objection, Amy Barber, a DNA analyst with the State police crime laboratory, was permitted to testify that a swab of the wire coat hanger contained a mixture of DNA from at least two people, but that it yielded inconclusive results with respect to the defendant. According to Barber, results for comparison with the defendant and Roberts were inconclusive, and Michael Jr. and Martin were excluded as potential sources. The prosecutor also introduced in evidence a chart of the alleles Barber had identified27 in testing swabs taken from the coat hanger and from various locations inside the truck.28 In response to cross-examination on the issue, Barber testified that she could not "make any inclusion or exclusion" because of the inconclusive results.

To support his claim that Barber should not have been permitted to testify about the inconclusive results, the defendant primarily relies on our decision in Commonwealth v. Mattei, 455 Mass. 840 (2010). In that case, we concluded that "expert testimony that DNA tests could not exclude the defendant as a potential source of DNA found at the crime scene, absent testimony regarding statistical findings explaining the import of such a result, [is] likely to confuse and mislead the jury." Id. at 842. However, we reiterated in that case the distinction between being unable to exclude a person as a potential source of DNA on the one hand, and having inconclusive test results on the other. See id. at 853-854, citing Commonwealth v. Mathews, 450 Mass. 858, 872 (2008), and Commonwealth v. Nesbitt, 452 Mass. 236, 253 (2008).

Where, as here, the testimony concerns inconclusive test results, admissibility is determined on a case-by-case basis, and turns largely on whether the defendant pursues a Bowden defense at trial. See Commonwealth v. Mathews, supra at 872. If the defendant has "call[ed] into question the integrity of the police investigation," id., quoting Bowden, supra at 485, "the prosecutor is entitled to introduce testimony to demonstrate that tests were performed and results (even if inconclusive) were obtained." Id. "In such circumstances, testimony regarding DNA test results, even those that are inconclusive, is relevant and probative to establishing the integrity and adequacy of the police investigation." Commonwealth v. Cavitt, 460 Mass. 617, 634-635 (2011). That was precisely the case here; as such, there was no error in allowing Barber to testify that DNA testing of the wire coat hanger had yielded inconclusive results.

Our decision in Commonwealth v. Buckman, 461 Mass. 24 (2011), cert. denied, 132 S.Ct. 2781 (2012) (Buckman), does not support the defendant's related claim, in reliance on that case, that the chart was erroneously admitted. In Buckman, supra at 34, we said that "the fact of, but not the details of, an inconclusive test result may be admitted to show the extent of the police investigation." Although the chart in question here contained "details of" the inconclusive test results, in that it identified certain alleles present in the DNA obtained from the wire, these are not the type of details to which our decision in Buckman was directed.

The prosecutor in Buckman had asked the expert a series of questions regarding whether "it would be possible for [the victim] to be the source of the DNA," and had elicited inculpatory testimony from the expert witness despite the inconclusive results. Id. at 33-34. Here, by contrast, the judge precluded the prosecutor from eliciting evidence that could suggest that there was any link between the inconclusive results and the defendant. She prevented the prosecutor from questioning Barber about those specific results and required that the witness be asked additional clarifying questions about the significance of an inconclusive result after the chart had been published to the jury.29 The judge's actions ensured that the witness's testimony would not mislead the jury into believing that any conclusions could be drawn from the data, and the prosecutor did nothing to undercut that position. See Commonwealth v. Cavitt, supra at 636 (nothing "implied that the defendant's DNA would have been found there if more of a sample had been present"). Although it would have been preferable to omit the inconclusive data from the chart, we cannot say that the judge abused her discretion in allowing it to be admitted.

7. Other claims. a. Jailhouse telephone call. The defendant challenges the seizure and admission in evidence of a recorded telephone call that he made to Spears while being held at the Cambridge jail awaiting trial. Before his first trial, the defendant moved to suppress the recording by arguing, inter alia, that he had a cognizable privacy interest in the contents of the telephone call, and that he was denied due process when the Middlesex County sheriff's department voluntarily provided the recording to State police. We have consistently rejected such an argument where, as here, all parties to the recorded conversation had notice that the call would be monitored or recorded. See Commonwealth v. Odgren, 455 Mass. 171, 188-189 (2009); Matter of a Grand Jury Subpoena, 454 Mass. 685, 687-688, 692-693 (2009); Cacicio v. Secretary of Pub. Safety, 422 Mass. 764, 772-773 (1996). Thus, the defendant's motion was properly denied.

b. Telephone call with Michele. The defendant maintains that the trial judge erred by prohibiting the admission of the defendant's statements during a recorded telephone call with Michele. When the conversation occurred on March 20, 2006, approximately one week after the shootings, the defendant was unaware that he was being recorded; Michele was cooperating with State police to secretly record the telephone call, which she placed while in New Hampshire. In the recording, the defendant repeatedly instructs Michele to be honest with the police about the extent of their relationship. At trial, he sought to admit these statements to demonstrate his state of mind and "consciousness of innocence." The judge concluded that the defendant's state of mind one week after the shootings was not relevant to any issue at trial, and that he was not entitled to introduce "consciousness of innocence" evidence. See Commonwealth v. Espada, 450 Mass. 687, 698 (2008) ("consciousness of innocence is of very little value, because there are a variety of different motives that can prompt action consistent with innocence"). The judge had broad discretion to exclude the statements, and we see no reason to disturb her ruling. See Commonwealth v. Simpson, 434 Mass. 570, 578-579 (2001) (evidentiary rulings "are matters entrusted to the trial judge's broad discretion and are not disturbed absent palpable error").

c. Expert testimony. The defendant argues, for the first time on appeal, that Nicole Spaun, an image analyst with the Federal Bureau of Investigation, was permitted to engage in "inconclusive speculation" when she testified as an expert regarding similarities between Martin's truck and the vehicle captured on surveillance footage near the scene of the shootings. The thrust of the defendant's argument is that, because the surveillance footage was admitted in evidence and available for the jury's independent review, the jury needed no assistance in deciding whether the vehicle depicted therein was in fact Martin's truck. See Commonwealth v. Pytou Heang, 458 Mass. 827, 844 (2011) ("purpose of expert testimony is to assist the trier of fact in understanding evidence or determining facts in areas where scientific, technical, or other specialized knowledge would be helpful"); Mass. G. Evid. § 702 (2012).

Trial judges have broad discretion in deciding whether to admit expert testimony. Commonwealth v. Federico, 425 Mass. 844, 847 (1997). Because this claim was raised for the first time on appeal, the trial judge was not afforded an opportunity to perform her role as a gatekeeper in assessing the reliability and utility of Spaun's testimony. Thus, because the defendant did not raise these concerns at trial, we have no basis in the record on which to conclude that the trial judge abused her discretion. See Commonwealth v. Arroyo, 442 Mass. 135, 145 (2004), quoting Commonwealth v. Sparks, 433 Mass. 654, 660 (2001) ("it is now too late to raise objections concerning the reliability of the testing and the conclusions reached"). Nothing in the record suggests that Spaun's testimony created a substantial likelihood of a miscarriage of justice.

8. Review under G. L. c. 278, § 33E. We have carefully reviewed the entire record of the case in accordance with our responsibility under G. L. c. 278, § 33E, and have found no basis on which to set aside or reduce the verdicts of murder in the first degree.

Judgments affirmed.