S.D. Codified Laws § 29A-3-409
After the time required for any notice has expired, upon proof of notice, and after any hearing that may be necessary, if the court finds that the testator is dead, venue is proper and that the proceeding was commenced within the limitation prescribed by § 29A-3-108, it shall determine the decedent's domicile at death, the decedent's heirs, and the decedent's testacy status. Any will found to be valid and unrevoked shall be formally probated. Termination of any previous informal appointment of a personal representative, which may be appropriate in view of the relief requested and findings, is governed by § 29A-3-612. The petition shall be dismissed or appropriate amendment allowed if the court is not satisfied that the alleged decedent is dead. A will from a foreign jurisdiction which does not provide for probate of a will after death, may be proved for probate in this state by a duly authenticated certificate of its legal custodian that the copy introduced is a true copy and that the will has become effective under the law of that jurisdiction.
SDCL 29A-3-409