§ N.H. Rev. Stat. § 667:18Resignation, Death, or Removal.

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A delegate to a constitutional convention may resign his or her office as such by filing his or her intention of resignation in writing with the secretary of state. The resignation shall become effective when approved in writing by the president of the constitutional convention. Whenever a delegate to a constitutional convention dies or moves from the district, town, or ward in which he or she was elected, the clerk of the town or of the city in which the delegate is a voter, or if the delegate is from an unincorporated place the clerk of the town in which he or she is registered, shall notify the secretary of state of the death or removal.

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