N.H. Rev. Stat. Ann. § 432:13

The governing body of the district shall consist of 5 supervisors appointed by the state conservation committee, who shall be land occupiers in the district. Associate supervisors, who shall be land occupiers in the district, shall be appointed by the governing body as deemed necessary and shall serve without vote when there is a quorum of supervisors present and voting. In the absence of a quorum, one or more associate supervisors may be designated by the chair to participate and to vote in place of any absent supervisors.