Visible crew/equipment: When we first see McClane on the snowmobile, marks from the camera snowmobile are visible. (01:27:20)
Visible crew/equipment: When we first go to the Annex Skywalk, the SWAT team are walking with the guy from the tower and he is talking on a radio. In the mirror behind them you can see the boom mike and operator as they walk.
Answer: In the first movie he's a New York cop visiting his wife. In the second Die Hard, he tells the airport officer that he's LAPD and moved there because of his wife's job. In the third Die Hard film, he most likely went back to New York because of marital problems and became a New York cop again.