The Palisades Parkway in NY is patrolled by the NYSP. In NJ it is patrolled by the Palisades Parkway Police.
The NYS Park Police may patrol the upper portions of the parkway where it is within the confines of Harriman State Park.
The Rockland Baracks is in Havestraw (Troop F Zone 2). The PIP is pretty much the only road they routinly patrol in Rockland as the Thruway and NY extension of the Garden State Parkway are Troop T's responsibility.