It was wise to call and get your insurance company involved because they will investigate the claim and determine if they will pay out on it. To make sure this is not a fake claim ask the people that sent you a letter to give you the name of the police station that you can go to and get a copy of the police report.

The best thing to do is be upfront and honest with the facts as you know them. This means to the police, if they come to your for your side of the incident, and your insurance company. It would be unwise to pay out any personal money to the people contacting you since so far there is no proof that you hit their vehicle. Your insurance company can handle it, that is one reason you need car insurance. If you don't want your insurance to pay the claim, then you should notify them. They may or may not oblige (for their protection). If they don't pay it because of your request, you should expect to appear in court to defend your reasons. You may want to get legal advice from a professional.

State statutes for hit and run vary by state. The basic definition is when a motorist knowingly leaves or flees the scene of a collision with another vehicle, property or human being. If you will be charged with a hit and run is up to the local law enforcement officers though.