N.H. Rev. Stat. Ann. § 546-B:4

Personal jurisdiction acquired by a tribunal of this state in a proceeding under this chapter or other law of this state relating to a support order continues as long as a tribunal of this state has continuing exclusive jurisdiction to modify its order or continuing jurisdiction to enforce its order as provided by RSA 546-B:7, RSA 546-B:8, and RSA 546-B:11-b.