N.D. Cent. Code § 40-08-08
If a vacancy occurs in a city council office by death, resignation, or otherwise, the city council may call a special city election to fill the vacancy for the unexpired term, or may, after fifteen days of the date of the vacancy appoint a person from the ward in which the council member previously holding was elected or appointed to fill the vacancy until the next city election, at which election the unexpired term must be filled. Upon petition of five percent of the qualified electors of the ward, as determined by the total number of votes cast in that ward in the last city general election, the council shall call a special election to fill a vacancy occurring more than six months before the next city election, if the petition has been submitted within fifteen days and before four p.m. of the fifteenth day of the date of the vacancy or of the vacancy being filled by appointment. If the petition is mailed, it must be in the possession of the council or its representative before four p.m. on the fifteenth day after the vacancy occurs or after the vacancy was filled by appointment.
N.D.C.C. § 40-08-08