Hit and Run unattended, claim after 1 year, should I take up with lawyer after allowing the insurance claim?

I got a call from an insurance company that I hit and unoccupied parked vehicle while i backed out on some date last year. They quoted a police dept case number and that a witness reported my car details it to the owner of the vehicle and to the police. I don't recall exactly but may have scratched the bumper while I backed out, I didn't realize then. It's been more than an year since the actual incident. If I allow my insurance company to pay them for the claim (I have coverage), would it be sufficient? Will the police arrest me for misdemeanor? Even if the insurance company pays them would the other party file case against me? The insurance guy said I need not contact the police or the other party for now. I am afraid it will affect my Visa status(I am non immigrant on work visa).