N.H. Rev. Stat. Ann. § 31:94-c

Any town, city or county which adopts the provisions of RSA 31:94-a may budget their receipts and expenditures, raise and appropriate revenues, and assess taxes on the basis of a single 18 month accounting period running from January 1 of the calendar year following adoption and ending June 30 of the next following year. Thereafter, they shall operate their fiscal affairs on the basis of a 12 month accounting period running from July 1 to June 30 of the next following year.