N.H. Rev. Stat. Ann. § 519:28

A court stenographer shall make for the use of the court and parties, after any trial, whenever ordered by the court, a true report of all proceedings, and the court may order the original notes to be filed. Upon request of either party, the original stenographic notes, and a duly certified copy of them written out in full, shall, as soon as practicable, be placed on file.