S.D. Codified Laws § 24-1-27

Upon notification of the death of any inmate who has not been released on parole or suspended sentence, an official of the Department of Corrections shall contact the county coroner, who shall proceed in accordance with the provisions of chapter 23-14. A department official shall also attempt to contact the person designated by the inmate prior to death or the next of kin, if known, and offer the body to be delivered to such person at that person's expense. If attempts to contact such persons fail or if the offer of delivery is declined, a department official, after forty-eight hours, shall make arrangements for the disposition of the body.