First things first. Report it to your insurance company right away. This claim will not cause your rates to go up if the guy backed into you and ran. Did you file a police report? Do you have a copy of said police report? Were you sitting in your car when this happened? Were you parked? If you try to sue the guy, one of the first things the court will say is that you have to "mitigate your damages" which means you need to report it to your own insurance company. Any lawyer will probably tell you this. Your insurance company will pay your claim, less a $200 uninsured motorist deductible, and pursue subrogation against the responsible party or his insurance company. If they recover from the other party, they will reimburse you the $200 UM deductible. Do you know the other guy's name and address? I'm just asking because that would tremendously help your insurance company.
If the cops did anything shady (judging from your original post they did), either you or your insurance company should report them to the FBI.