N.H. Rev. Stat. Ann. § 517:14-d

The date fixed for the deposition shall be no more than fourteen days from the time the petition is received by the clerk of court except that this time may be extended upon request of the prosecution only. Notice of the court's order, together with a copy of the original petition filed by the prosecution, shall be served upon the defendant and his counsel at least 72 hours before the time fixed for the taking of the deposition.