If you can make a case with the police, they'll let you know. If you simply want to find out if this car has ever got into any accidents, then you can pay $25 to do a vin number search.
My mom got in an accident with a young guy, they exchanged driver info, but it turned out to be fake, all fake. Luckily my mom wrote down the license plate number and reported the incident to the police, and the police quickly located the offender. The young guy is now being charged by the police, court proceeding will follow, and my mom will be prosecutor's witness.