§ N.H. Rev. Stat. § 661:6United States Representative.

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If a vacancy occurs in the office of United States representative, the governor with advice of council shall, as soon as practicable, have precepts issued to the selectmen of the towns and cities in the district where the vacancy exists directing them to call a special state general election on the day he designates to fill the vacancy. Such election shall be conducted as provided in RSA 661:11 and shall fill the vacancy for the unexpired term.

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