N.H. Rev. Stat. Ann. § 227-H:15

If an abatement is granted, the commissioner of revenue administration shall certify the fact and the amount to the state treasurer, who shall account to the town for such abatement out of any funds in the treasury not otherwise appropriated. In case the amount so certified by the commissioner of revenue administration shall be greater than the state tax assessed against the town, the excess shall be paid to the town by the state treasurer out of any funds in the treasury not otherwise appropriated, upon the approval of the governor and council.