N.H. Rev. Stat. § 6:8-a

The treasurer is authorized to enter into an agreement with a bank or banks for the purpose of providing a payment and custodial service for bonds and coupons issued by the state. The agreement shall provide that the said bank or banks will maintain an accounting of all bonds and coupons paid and will provide periodic statements indicating the unpaid items. The agreement shall further provide that the bank or banks will hold the paid bonds and coupons until they may be destroyed pursuant to this section. After the close of each fiscal year, the bank or banks shall provide for the destruction of those bonds and coupons which were paid in the fiscal year ending one year prior to the fiscal year just closed and shall file a destruction certificate with the state treasurer and the secretary of state.