I live on the State Line CA/AZ (the line is the river which is in my back yard, that's how close it is!), and about six months ago, I saw a CA CHP, following a NM car from about 5 miles in CA, all the way across the State Line into AZ, where he pulled him over. I was shocked!
Came home and called a friend in AZHP, and was told that they have an agreement with all neighboring states to pursue into the neighboring state for 20 miles. If the pursuit does not end in 20 miles, the neighboring state HP will take over!
So if this is done between the states, I can imagine it be even easier between the counties/boroughs.
The old days of "running the line" are over.