We have a back loop for our parking lot that is intended for staff, but the public is not prohibited there. We do have "library only" signs, and since we're adjacent to a popular park and walking trail, our signs have some additional language about those (photo attached). Last summer the overnight parking was starting to be a problem, but the local towing company wouldn't tow someone from our lot until we had signs posted at our parking lot entries, indicating no overnight parking under threat of towing, with the towing company and their phone number listed.
I have those signs but didn't get them in before the ground froze, so they're waiting until better weather. In the meantime, this winter we haven't had any problems with overnighters, and we don't patrol to be sure people aren't parking in our lot and heading over to the park/trail (I know some are doing it, and while we have an extremely busy parking lot, they use a corner that is the last to fill up anyway).
I hope that helps!