Generally an attorney wanting to contact a Corporation's Insurer would write a letter to the Corporation putting them on notice of the claim and asking them to forward the letter to the Corporation's insurer. Many companies will respond to that type of a letter. If the Corporation is self insured they may respond directly or they will usually forward the letter to their insurance company and you would hear from the insurer. It is always wise however to contact an attorney in your location for advice before writing any letters. What you say could be used later on and an attorney who is experienced would know what to include in such a letter and what not to say. Once a letter is sent by you it is too late to change what was said later on. For contact information for a Corporation you can contact the Secretary of State's office in CT on a website called Concord. Good luck with your claim and again I would strongly advise seeing an attorney at the outset before writing any letters yourself. It is always important to see an attorney as soon as possible after any injury because of statutes of limitations which could limit your ability to file a claim if you wait too long.
I hope this information helps you.
Consider consulting with a personal injury attorney—with a confidential consultation. Many times personal injury attorneys will take cases on contingency where the client will not have to pay anything until money is recovered, part of the recovery goes to the attorney and part of the recovery goes to the client (if an attorney takes your case the attorney will fully describe the fee structure).
Some personal injury attorneys might know (or have a best guess) from experience, because they have litigated against the same corporation.
This answer contains generalizations and there are many caveats. Hire an attorney when appropriate for your personal set of facts.