N.H. Rev. Stat. Ann. § 507:13

Whenever in any case the venue is changed by order of court, and the case is tried by a jury in the county to which it is transferred, such county shall have judgment and execution against the county from which it is transferred for the fees due jurors, sheriffs and the stenographer for travel, attendance and services while engaged in such trial, to be taxed, allowed and entered by the presiding justice.