S.D. Codified Laws § 21-27-18.1
A final judgment or order entered under this chapter may not be reviewed by the Supreme Court of this state on appeal unless the circuit judge who renders the judgment or a justice of the Supreme Court issues a certificate of probable cause that an appealable issue exists. A motion seeking issuance of a certificate of probable cause shall be filed within thirty days from the date the final judgment or order is entered. The issuance or refusal to issue a certificate of probable cause is not appealable. However, a party may, upon the circuit court judge's refusal to issue a certificate of probable cause, file a separate motion for issuance of a certificate of probable cause with the Supreme Court within twenty days of the entry of the circuit judge's refusal. Any party filing a motion with the Supreme Court shall serve a copy of the motion upon the opposing party, who shall have ten days to respond. The applying party shall then have five days to reply to such response. If a certificate of probable cause is issued the appeal may be brought by an applicant or the state within thirty days after entry of the certificate of probable cause.
Service of either a motion for a certificate of probable cause or of an appeal must be made upon both the attorney general and the appropriate state's attorney when the motion is made or the appeal is taken by the party seeking the habeas corpus relief.
SDCL 21-27-18.1