§ 30.02  VACANCIES.
   (A)   A vacancy that occurs in an elective office of the town shall be filled by appointment of the town.  If the term of the office expires immediately following the next regular town election or if the next regular town election will be held within 90 days after the vacancy occurs, the person appointed to fill the vacancy shall serve the remainder of the unexpired term.  Otherwise, a successor shall be elected at the next regularly scheduled town election that is held more than 90 days after the vacancy occurs, and the person appointed to fill the vacancy shall serve only until the elected successor takes office.  The elected successor shall then serve the remainder of the unexpired term.  If the number of vacancies of the Board is such that a quorum of the Board cannot be obtained, the Mayor shall appoint enough members to make up a quorum and the Board shall then proceed to fill the remaining vacancies.
   (B)   If the number of vacancies on the Board is such that a quorum of the Board cannot be obtained and the Office of Mayor is vacant, the Governor may fill the vacancies upon the request of any remaining member of the Board upon the petition of any five registered voters of the town.
(G.S. § 160A-63)  (1988 Code, § 30.02)