All States that I'm aware of have compacts (or other legal agreements) that allow for bordering states to pursue from across the border. Same goes for cities.
This comes down to the jurisdictional agreements, departmental SOP, and the type of violation.
Most traffic offenses are "civil" in nature (not criminal) and therefore the evidence needs only be a "preponderence" and not "beyond reasonable doubt". This happens all the time; lots of examples that have enforcement that goes over a bridge, across a line, etc. The "event" needs only be documented and filed in the jurisdiction that it occurred. Where the "stop" takes place for an infraction isn't going to come into play. The NY cop can pull someone over in PA to issue a NY citation for an event that occurred in NY, and no court is going to blink an eye. That is true of all states, and counties, and cities and towns ...
Where it does get more involved is if a crime is later detected at the stop itself. Say the officer from NY gets you pulled over for speeding in PA, and discovers that you're suspended, or drunk, or in possession of stolen "xyz", or wanted on a warrant, or whatever ... He has two choices:
1) call for PA response, have them incarcerate you with a hold for extradition, and file to get you back into NY (because he witnessed you in NY, therefore the crime did occur there)
2) call for PA response, have them arrest you in PA jurisdiction, and use his PC for the stop as the basis for contact (his contact is the basis for their arrest; it's been legally done before many times and ruled not a violation of Rights)
Where is gets more interesting is if crimes occur during the pursuit itself. Say someone robs a bank in NY along the border, but flees to PA. Along the way, he's being pursued in flight by NY. And he commits not only the crime of origin, but crimes of wreckless driving, felony fleeing, property destruction, etc. He'll end up being arrested in both NY and PA, but he'll go to incarceration where he's caught (in this case, PA). But because he did crimes in both states (because it was a real "pursuit" with multi-agencies and becomes one of those TV-worthy events), then he'll have the joy of being prosecuted in both places for the crimes which occurred in each.
This is not a new topic by any means; it's been covered in LEO for decades. There are a bazillion municipalities that straddle a border between counties and even states. Places like Louisville KY are 100% in KY, but the populous moves back-and-forth across into IN for work and home all the time. Places like the "Region" in Indiana deal with this all the time; Hammond, Munster, Calumet City, Lansing, etc all utilize the ability of LEOs to go across a state line. There are places where you cannot even tell whatsoever where the line is, unless you're from the area.
This is a must-have in terms of useful enforcement. It if were not so, a "criminal" could just hop over a border and get away Scot-Free. I cannot think of a State that does not have some type of mutual-aid and pursuit agreement.
The difference is the type of event. Civil infractions are not going to involve the second entity; it's only a place to pull over and deliver the citation. Crimes, OTOH, will incur jurisdictional cooperation.
