N.H. Rev. Stat. Ann. § 6-A:9

Any bonds or notes issued pursuant to this chapter, if properly executed by the officers of the state in office on the date of the signing or on the date of imprinting of the facsimile signature, as the case may be, shall be valid and binding according to their terms notwithstanding that before delivery thereof and payment therefor any or all such officers shall have for any reason ceased to hold office.