New Jersey Statutes Title 38A. Military and Veterans Law 38A § 16-1

(a) Upon the request of the Governor of another State, the Governor of this State, may, in his discretion, order any portion or all of such forces to assist the military, naval or police forces of such other State who are actually engaged in defending such other State. Such forces may be recalled by the Governor at his discretion.

(b) Any organization, unit, detachment or member of such forces, upon order of the officer in immediate command thereof, may continue in fresh pursuit of insurrectionists, saboteurs, enemies or enemy forces beyond the borders of this State into another State until they are apprehended or captured by such organization, unit, detachment or member or until the military, naval or police forces of the other State or the forces of the United States have had a reasonable opportunity to take up the pursuit or to apprehend or capture such persons; provided, such other State shall have given authority by law for such pursuit by such forces of this State. Any such person who shall be apprehended or captured in such other State by an organization, unit, detachment or member of the forces of this State shall without unnecessary delay be surrendered to the military, naval or police forces of the State in which he is taken or to the United States, but such surrender shall not constitute a waiver by this State of its right to extradite or prosecute such person for any crime committed in this State.