S.D. Codified Laws § 15-30-1
Whenever, after appeal to the Supreme Court, it shall appear to the satisfaction of the Supreme Court upon application of a party that the ends of justice require that such party should be permitted to make a motion for a new trial for a cause set forth in subdivision 15-6-59(a)(1), (2), (3), or (4), and that sufficient excuse exists for not having made said motion prior to the appeal, the Supreme Court may remand the record to the trial court for the purpose of making such motion, but no such remand shall be made unless such motion can be made and hearing thereon had in the trial court within sixty days from and after the date on which the time for appeal commences unless the Supreme Court extends the time for good cause shown.
SDCL 15-30-1