As I am not licensed in your state, I can only provide you with general information. You should probably try to file a police report. Police are called to the scene of accidents on private property all the time (i.e. Wal-Mart parking lots for example).
If you have collision damage coverage on your own car, it may be easier to pursue the claim through your own carrier. Your carrier will then pursue the adverse driver and his insurance company. Failing that, you may be able to file suit against the adverse driver in small claims court, of course depending on the jurisdictional limit of your small claims court.
Generally it is advisable to contact the police any time you or your vehicle are Involved in any type of collision.
Sign up to receive a 3-part series of useful information and advice about personal injury law.