N.H. Rev. Stat. Ann. § 597:28

Sureties may be discharged before forfeiture of the recognizance by committing the principal to the jail of the county, by leaving with the jailer a certified copy of the order to recognize and of the names of the bail, and a certificate of the bail thereon that they have committed the principal in discharge of their liability as bail, and by giving written notice thereof to the attorney general or county attorney.