N.H. Rev. Stat. Ann. § 289:16

The governing body may, at the expense of the municipality, disinter all the remains of persons buried in such cemetery and reinter the same in the unoccupied part of another cemetery within the municipality, such reinterment to be in the place designated by the nearest surviving relatives of the deceased persons or, in the absence of such surviving relative, by the cemetery trustees. Such removal and reinterment shall be done prudently and with proper care and attention.