N.H. Rev. Stat. Ann. § 509:11

Writs issued by justices of municipal and district courts shall be under seal and directed to the sheriff of any county or his deputy or to any constable of any town in the county, or to either of said officers; provided, however, that writs of attachment shall be directed to the sheriff of any county, or to any such constable, or to the plaintiff, his attorney or any other person.