Is it possible to trace an I pad with a serial number?
Not really. However, as mentioned, you could go to an apple store with your original purchase receipt and identification that matches that receipt and see if they were silly enough to try to re-register the device with their name, email and/or phone number. Then you could take that information to the police.
I'm assuming you didn't have "find my ipad" turned on. In that case, you could just jump on icloud.com and punch in the same userid and password and track it from there (and probably still let the police take care of it).