When a vacancy occurs in the board of county commissioners, the remaining members of the board immediately shall appoint some suitable person to fill the vacancy from the district in which the vacancy occurred. If a majority of the officers fails to agree upon a person to fill the vacancy, the county treasurer or, if the county does not have an elected treasurer, another elective county officer must be called in and shall act as an additional member of the board to fill the vacancy. The appointee holds office until the appointee's successor is elected at the next general election that occurs at least ninety-five days after the vacancy and the successor has qualified.
N.D.C.C. § 44-02-05