N.H. Rev. Stat. Ann. § 292:5-b

A foreign nonprofit corporation established for any of the purposes set forth in RSA 292:1 or for a substantially similar purpose, desiring to do business in this state in furtherance of such purpose for the benefit of citizens of this state, may register as a foreign corporation by making application as provided in RSA 293-A:15.03, excepting those portions relative to using a form of the words "corporation," "company," "incorporated" or "limited" in the corporate name. Any such foreign nonprofit corporation shall file the return and pay the fee provided in RSA 292:25-29.