A lost Apple watch has been turned in to the police department where I work. Of course, it is locked. Is there any way for me to find out who the owner is?
Only if the owner decides to put it into Lost Mode. See the 'Put your Apple Watch in Lost Mode' section in:
If your Apple Watch is lost or stolen - Apple Support
Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else.