Ohio Rev. Code Ann. § 2949.03

If a judgment of conviction by a court of common pleas, municipal court, or county court is affirmed by a court of appeals and remanded to the trial court for execution of the sentence or judgment imposed, and the person so convicted gives notice of his intention to file a notice of appeal to the supreme court, the trial court, on the filing of a motion by such person within three days after the rendition by the court of appeals of the judgment of affirmation, may further suspend, subject to division (A)(2)(b) of section 2953.09 of the Revised Code, the execution of the sentence or judgment imposed for a time sufficient to give such person an opportunity to file a notice of appeal to the supreme court, but the sentence or judgment imposed shall not be suspended more than thirty days for that purpose.