N.H. Rev. Stat. § 655:38
If a candidate to be voted for at the general election shall make oath between the date of the candidate's nomination and the day of the election that he or she does not qualify for the public office which he or she seeks because of age, domicile, or incapacitating physical or mental disability acquired subsequent to the primary, the secretary of state may remove said person's name from the ballot. Any such oath citing an incapacitating physical or mental disability shall be accompanied by a letter from a licensed physician confirming such a condition. A new candidate may be substituted by the appropriate party committee by submitting the name of the new candidate to the secretary of state within 3 days of the notice of disqualification. The name of the substitute candidate shall be placed on the ballots as provided in RSA 656:21.
RSA 655:38
1979, 436:1. 2000, 12:1. 2009, 214:4. 2013, 228:1, eff. Sept. 13, 2013.