N.H. Rev. Stat. § 659:91
Any person who is nominated by the same political party for incompatible offices shall notify the secretary of state in person, in writing, by facsimile transmission, or by e-mailing a signed statement as an attachment no later than the Friday following the date of the primary of which nomination he or she will accept. Thereupon the secretary of state shall declare a vacancy to exist in the nomination which such person declined. The vacancy shall be filled as provided in RSA 655:37 except that all the necessary declarations of candidacy and affidavits shall be filed no later than 5:00 p.m. on the first Tuesday following the date of the primary.
RSA 659:91
1979, 436:1. 1981, 240:4. 1983, 426:19. 1994, 4:19. 2010, 317:53. 2012, 113:9, eff. May 31, 2012.