N.H. Rev. Stat. Ann. § 597:40

If a person is arrested in one county on a warrant for an offense alleged to have been committed in another county exceeding the jurisdiction of a justice to determine, the officer, on the arrestee's request, shall take the arrestee before a justice for the county or judicial district thereof in which the arrest was made, and, upon the arrestee's waiving examination, such justice may take the arrestee's personal recognizance or recognizance with sufficient sureties upon the terms and conditions prescribed by this chapter for the arrestee's appearance at the next term of the superior court for the county or judicial district thereof in which the offense is alleged to have been committed, and the arrestee shall return to said court certified copies of the warrant and recognizance.