N.H. Rev. Stat. § 6:12-a

Whenever it shall appear that a state department or agency has in the course of its administration received funds from sources outside the state treasury designated as revenue, which said funds have been paid into the treasury, and it is later found that certain of said revenue so paid in is in excess of the amounts which should legally be paid to the state, the head of the department or agency concerned may certify the facts of such excess revenue to the commissioner of administrative services and request a repayment thereof to the persons entitled thereto. The governor, with the consent of the council, may, in such instances, draw his warrants for the repayment of such excess revenue from funds in the treasury not otherwise appropriated and the commissioner of administrative services and the treasurer shall credit such repayments to the proper revenue item for the department or agency concerned.