If one single action is a violation of both a state statute and a federal statute then both crimes can be prosecuted against the same individual in state court and in federal court. The same is true if a member of the armed services violates a provision of the uniform code of military Justice (perhaps drunk driving while on base) and also violates state laws against her driving. The key is that there are two different jurisdictions bringing the charges.
If one single action is a violation of both a state statute and a federal statute then both crimes can be prosecuted against the same individual in state court and in federal court. The same is true if a member of the armed services violates a provision of the uniform code of military Justice (perhaps drunk driving while on base) and also violates state laws against her driving. The key is that there are two different jurisdictions bringing the charges.