N.H. Rev. Stat. Ann. § 265:149

Any city or town shall have the power to make ordinances, bylaws or regulations respecting the use and equipment of bicycles, except mopeds as defined in RSA 259:57, on its ways, provided that any such ordinances, bylaws or regulations enacted with respect to such equipment shall be at least as stringent as the requirements of RSA 266:85-89. Any city or town may require that bicycles, except mopeds as defined in RSA 259:57, be licensed and may charge reasonable fees for such licensing.