How do I find out someone's insurance company

I am the victim of a hit and run that took place in a private parking lot. I was not present when the accident took place but there was a witness which got the tag number and make and model of the vehicle I was able to get a name and address of the person but that was it. When I called the police they said they do not come out for private property accidents but sent me a crash form to mail in. I really do not want to file a claim with my insurance because I do not want this to raise my rates.
How do I go about getting the insurance information on this person with the info I have?