N.H. Rev. Stat. Ann. § 16:2

There shall be filed with the secretary of state a petition for the calling of a special session of the general court which petition shall be signed by not less than 50 members of the house of representatives, not more than 10 of whom shall reside in the same county, and signed by not less than 8 members of the senate. Said petition shall state the reason or reasons why the public welfare requires a special session of the general court.