A ticket/fine in and of itself will never appear on your credit.
However, many cities/counties will eventually sell these unpaid tickets/fines to a collection agency, and that collection agency then has the right to report its collection on your credit. These are bound by similar statute-of-limitation regulations as regular (credit card) debts. In rare cases, there can even be judgments issued for nonpayment of tickets/fines which can worm their way into a person's public records section, but that is highly unusual in most states.
Unpaid tickets/fines can also affect things like driver's license renewals, vehicle registration renewals, and other things that are not part of your credit file but still can be a painn in the rear to deal with. Some types can result in bench warrants, seized vehicles, and other headaches too, depending on the original violation and the code in your municipality.
If it was mine, I'd just figure out how to pay it and get it to go away before it has any chance to get to another level. It won't suddenly appear on your credit, and you won't have to be worried about it while you deal with your rebuild - that's enough stress for one person to deal with.
