N.H. Rev. Stat. Ann. § 482:66

A special town or village water district meeting or town council meeting to authorize action under this subdivision may be called by the local legislative body by posting or causing to be posted a written or printed copy of the warrant noticing such meeting at the place of meeting and at 2 other public places in the town at least 7 days prior to holding the meeting, including the day of holding such meeting. The local legislative body shall leave, on or before the day of the meeting, a copy of such warrant with the town clerk, who shall record it. Upon petition of 25 taxpayers, the local legislative body shall call a special town meeting or town council meeting to consider action under this subdivision.