Ohio Revised Code Title XXIX. Crimes Procedure § 2953.02

In a capital case in which a sentence of death is imposed for an offense committed before January 1, 1995, and in any other criminal case, including a conviction for the violation of an ordinance of a municipal corporation, the judgment or final order of a court of record inferior to the court of appeals may be reviewed in the court of appeals. A final order of an administrative officer or agency may be reviewed in the court of common pleas. A judgment or final order of the court of appeals involving a question arising under the Constitution of the United States or of this state may be appealed to the supreme court as a matter of right. This right of appeal from judgments and final orders of the court of appeals shall extend to cases in which a sentence of death is imposed for an offense committed before January 1, 1995, and in which the death penalty has been affirmed, felony cases in which the supreme court has directed the court of appeals to certify its record, and in all other criminal cases of public or general interest wherein the supreme court has granted a motion to certify the record of the court of appeals. In a capital case in which a sentence of death is imposed for an offense committed on or after January 1, 1995, the judgment or final order may be appealed from the trial court directly to the supreme court as a matter of right. The supreme court in criminal cases shall not be required to determine as to the weight of the evidence, except that, in cases in which a sentence of death is imposed for an offense committed on or after January 1, 1995, and in which the question of the weight of the evidence to support the judgment has been raised on appeal, the supreme court shall determine as to the weight of the evidence to support the judgment and shall determine as to the weight of the evidence to support the sentence of death as provided in section 2929.05 of the Revised Code.