When mine was stolen I was later notified by a friend who recognized it. I arrived and locked it up and the "current owner" decided to stick around and argue until the police arrived. I had documentation in my wallet of the police report with the serial number to prove it was mine (I'd carried that piece of paper for over a year, just in case) and the fellow was arrested and charged with possession of stolen property while I was permitted to take my bike home. He had to go to court. I knew he probably was not the thief but he probably purchased from one. Case was dismissed.

If the police are interested in pursuing this on your behalf, I'd be very much surprised. Good luck!