S.D. Codified Laws § 23A-27A-31
If the time period for the execution of any defendant in a capital case has passed by reason of a stay of proceedings incident to appellate review or by reason of the issuance of a writ of habeas corpus, certiorari, or other original remedial writ of the Supreme Court, or for any other reason, the sentencing court shall issue a warrant of death sentence and execution in accordance with § 23A-27A-15 appointing a new week for the execution of the original sentence without requiring the defendant to be brought before the sentencing court. Upon its issuance, the clerk of the court in which the sentence was pronounced shall immediately send a certified copy of the warrant of death sentence and execution to all attorneys of record, to the warden having custody of the defendant, to the secretary of corrections, and to the Governor. The warden shall execute the warrant of death sentence and execution accordingly. This procedure applies to any case in which the time period for carrying out the original warrant of death sentence and execution has elapsed without regard to whether the original warrant was issued prior or subsequent to July 1, 1998.
SDCL 23A-27A-31