S.D. Codified Laws § 21-25B-19
If any person serving on a health care services arbitration panel becomes disabled or is disqualified from service thereon for any reason, the presiding judge of the circuit court shall, upon petition of any party to the arbitration agreement on the controversy under consideration, within fifteen days appoint someone to fill such vacancy. The person appointed to fill a vacancy shall have made available to him all exhibits and testimony heard or introduced prior to his appointment. If the vacancy is a position originally appointed by one of the parties to the controversy, on making such appointment the court shall consider persons recommended by the party originally making the nomination for the position vacated, but the court shall not be bound by any such recommendation.
SDCL 21-25B-19