S.D. Codified Laws § 15-26A-56

If anything material to either party is omitted from the record, is misstated therein, or is improper, the parties by stipulation, or the trial court, before the record is transmitted to the Supreme Court, or the Supreme Court, on motion by a party or on its own initiative, may direct the record be corrected and if necessary require a supplemental record be approved and transmitted.