It’s hard to say for sure because these things, the statutes, what the state DMV does and what is left to local authorities, vary from state to state, and you don’t mention what state you’re in but I would think the answer would be yes, the DMV in the other county would have your parking ticket records, in most if not all states they would be, I think, but like I said, there’s no way to know for sure. There might be information on your state DMV’s website about whether or not parking tickets are reported to the DMV or not. Anyway, your tags are expired already? I guess you could give trying to register your car in the other county and you either will be able to or you won’t.