N.H. Rev. Stat. § 105:13-a
The authority of any duly authorized certified police officer of a municipality located near the border of a neighboring state shall extend to any other municipality in the other state also located near such border, provided that the chief law enforcement officer of the requesting municipality has executed with the chief law enforcement officer of the responding municipality a written agreement which sets forth the terms and conditions under which such assistance may be requested or rendered. The executed agreement shall constitute authorization for every request for assistance, and for any assistance rendered in accordance with the terms and conditions of the written agreement, regardless of whether the responding police officer is named in the agreement. In an emergency situation, the ranking on-duty law enforcement official of the municipality is authorized to make an oral request for assistance to the ranking on-duty law enforcement official in the responding municipality, subject to the terms and conditions of such written agreement, and the authority of the responding police officer shall extend to the requesting municipality. The written agreement shall remain in full force and effect until terminated by the mutual consent of the chief law enforcement officers of each municipality, or until 10 days after the chief law enforcement officer of one municipality has received notification from the chief law enforcement officer of the other municipality of his intention to terminate.
RSA 105:13-a
1988, 70:1.