Ok, so you contacted the police and made a report, that is good. Are you putting a claim in on your insurance? If so, don't worry about it, they will try to find the owner of the car and will sue them for the damages.
If not, well then you will just have to see what the police will do.
I have never done it, but I have heard you can go to a DMV and they "may" look up information from the license plate number. Not sure how much it is for the search, but I do believe they will do it.