Ohio Rev. Code § 2953.10
When an appeal is taken from a court of appeals to the supreme court, the supreme court has the same power and authority to suspend the execution of sentence during the pendency of the appeal and admit the defendant to bail as does the court of appeals unless another section of the Revised Code or the Rules of Practice of the Supreme Court specify a distinct bail or suspension of sentence authority.
When an appeal in a case in which a sentence of death is imposed for an offense committed on or after January 1, 1995, is taken directly from the trial court to the supreme court, the supreme court has the same power and authority to suspend the execution of the sentence during the pendency of the appeal and admit the defendant to bail as does the court of appeals for cases in which a sentence of death is imposed for an offense committed before January 1, 1995, unless another section of the Revised Code or the Rules of Practice of the Supreme Court specify a distinct bail or suspension of sentence authority.
R.C. §2953.10