Upon the filing of any petition referred to in § 15-26A-13 with the clerk of the Supreme Court, the petitioner may make application to the court for a stay of proceedings pending action of the court on such petition. The court shall grant such stay only when satisfied that the ends of justice require it, and upon such security as the court may direct to safeguard any other party against damage by reason of delay. If the court makes an order granting such stay, a certified copy thereof must be filed with the clerk of the court from which the appeal is sought. The filing of the petition shall not operate to stay proceedings except as provided in this section.
SDCL 15-26A-19