How can police find out if you stole a computer?

Every computer should have a unique MAC identifier. When the computer is connected to the internet it is possible to query the computer remotely and get that MAC identifier. If you stole the computer and the legal owner has a record of that identifier, it provides proof that the computer you are using is the one they had stolen - and it can be traced back to you. Obviously all the other ways of detecting theft apply - confession, someone seeing you stealing it, leaving evidence behind, trying to pawn it, etc.