N.H. Rev. Stat. § 111:12
Any military forces or organization, unit or detachment thereof, of another state who are in fresh pursuit of insurrectionists, saboteurs, enemies or enemy forces may continue such pursuit into this state until the military or police forces of this 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 and are hereby authorized to arrest or capture such persons within this state while in fresh pursuit. Any such person who shall be captured or arrested by the military forces of such other state while in this state shall without unnecessary delay be surrendered to the military or police forces of this state to be dealt with according to law. This section shall not be construed so as to make unlawful any arrest in this state which would otherwise be lawful; and nothing contained in this section shall be deemed to repeal any other statutory provisions relating to the fresh pursuit of criminals.
RSA 111:12
1941, 46:12. RL 144:12. RSA 111:12. 1981, 327:6, eff. Aug. 16, 1981.