N.H. Rev. Stat. Ann. § 674:46

For the purpose of this subdivision, the local legislative body of any city, town, or county in which there are located unincorporated towns or unorganized places shall have the authority, by ordinance, to establish, change, lay out and define historic districts. Within the district, the municipality is empowered to regulate the construction, alteration, repair, moving, demolition or use of such structures and places.