SDCL § 4-1-5: Disqualification of member of board--Selection of replacement.

If any member of the Board of Finance determines himself disqualified from acting on any matter considered under the provisions of this chapter, he shall notify the board of his determination in writing. Upon receipt of the determination of disqualification, the remaining members of the Board of Finance shall select, by a majority vote, a replacement. The individual selected to replace a disqualified member of the Board of Finance shall have all the powers and duties of a regular member of the board with respect to the matter before the board that caused the regular member to disqualify himself.