N.H. Rev. Stat. Ann. § 45:7

The mayor thus chosen and qualified shall be the chief executive officer of the city, and for the preservation of the peace shall have the powers of sheriff and conservator of the peace, and, in case of any unlawful assembly, may appoint as many special constables as he may think expedient, giving to each such badge of office as the city councils have designated or as he shall designate.