N.H. Rev. Stat. Ann. § 455:15

Any commissioner for any other state who is authorized to take depositions, administer oaths and affirmations and take the acknowledgment of deeds within this state, to be used in such other state, and any commissioner appointed by the supreme or superior court or any justice thereof, shall have the power to administer oaths and affirmations, to issue writs of summons to a witness, to proceed against such witness upon his neglect to appear and give his deposition, and in all proceedings under his commission, that is vested in justices of the peace in like cases.