N.H. Rev. Stat. § 39:3
Upon the written application of 25 or more registered voters or 2 percent of the registered voters in town, whichever is less, although in no event shall fewer than 10 registered voters be sufficient, presented to the selectmen or one of them not later than the fifth Tuesday before the day prescribed for an annual meeting, the selectmen shall insert in their warrant for such meeting the petitioned article with only such minor textual changes as may be required. Such corrections shall not in any way change the intended effect of the article as presented in the original language of the petition. For the purposes of this section, the number of registered voters in a town shall be the number of voters registered prior to the last state general election. The right to have an article inserted in the warrant conferred by this section shall not be invalidated by the provisions of RSA 32. In towns with fewer than 10,000 inhabitants upon the written application of 50 or more voters or 1/4 of the voters in town, whichever is fewer, and in towns with 10,000 or more inhabitants upon the written application of 5 percent of the registered voters in the town, so presented not less than 60 days before the next annual meeting, the selectmen shall warn a special meeting to act upon any question specified in such application. The checklist for an annual or special town meeting shall be corrected by the supervisors of the checklist as provided in RSA 654:25-31. Those persons qualified to vote whose names are on the corrected checklist shall be entitled to vote at the meeting. The same checklist used at a recessed town meeting shall be used at any reconvened session of the same town meeting. In no event shall a special town meeting be held on the biennial election day.
RSA 39:3
RS 32:3. CS 34:3. GS 35:3. GL 38:3. PS 41:3. PL 45 :3. 1937, 40:1. RL 57:3. 1947, 21:1. RSA 39:3. 1969, 59:1. 1971, 79:1. 1975, 160:1. 1981, 454:1. 1987, 299:1. 1990, 192:1. 1991, 223:1; 370:5. 1994, 197:1, eff. July 23, 1994. 1998, 194:1, eff. Aug. 17, 1998. 2018, 325 : 1 , eff. Aug. 24, 2018.