S.D. Codified Laws § 21-27-23
Current with legislation signed by the governor on or before 3/6/2024
Where the writ of habeas corpus is refused, or where the writ is discharged after having been issued, and the prisoner has been denied bail, he may be admitted to bail by the Supreme Court or one of the judges thereof, pending appellate review.
SDCL 21-27-23