N.H. Rev. Stat. Ann. § 87:18

An inventory and appraisal under oath of the whole of every estate, any part of which may be subject to a tax hereunder, in the form prescribed by the probate court, shall be filed in probate court by the executor, administrator, or trustee within 3 months after appointment and a copy of such inventory shall be provided to the department of revenue administration by the executor, administrator, or trustee at such time.