N.H. Rev. Stat. § 12-G:41

All towns and cities within the confines of which there are ports, harbors, or navigable tide rivers of the state which are subject to the jurisdiction of the authority, or the division acting on behalf of the authority, shall retain all the powers of such town or city relative to such ports, harbors, and navigable tide rivers and the lands abutting the same, excluding lands located within the boundaries of the former Pease Air Force Base, so long as the authority has not by positive action or definite rule or regulation preempted the jurisdiction hereof. No town or city shall have any jurisdiction over the land or activities at the former Pease Air Force Base except as specifically authorized under other provisions of this chapter, provided, however, that in and over all such lands, jurisdiction of cases involving violations of federal law by a child shall be concurrent and shall be assumed only if waived by the federal court or a United States attorney.