Ohio Rev. Code § 313.09
The coroner shall keep a complete record of and shall fill in the cause of death on the death certificate, in all cases coming under his jurisdiction. All records shall be kept in the office of the coroner, but, if no such office is maintained, then such records shall be kept in the office of the clerk of the court of common pleas. Such records shall be properly indexed, and shall state the name, if known, of every deceased person as described in section 313.12 of the Revised Code, the place where the body was found, date of death, cause of death, and all other available information. The report of the coroner and the detailed findings of the autopsy shall be attached to the report of each case. The coroner shall promptly deliver, to the prosecuting attorney of the county in which such death occurred, copies of all necessary records relating to every death in which, in the judgment of the coroner or prosecuting attorney, further investigation is advisable. The sheriff of the county, the police of the city, the constable of the township, or marshal of the village in which the death occurred may be requested to furnish more information or make further investigation when requested by the coroner or his deputy. The prosecuting attorney may obtain copies of records and such other information as is necessary from the office of the coroner. All records of the coroner are the property of the county.
R.C. §313.09