Ohio Rev. Code § 3705.05
In each primary registration district, the board of health of the health district, on the recommendation of the health commissioner, shall appoint the local registrar of vital statistics. When a state hospital or other public institution has been made a primary registration district, the superintendent, or other person in charge thereof, shall be the local registrar of such district. When two or more primary registration districts have been combined into one primary registration district, the health commissioners of the health districts that constitute the combined primary registration district shall jointly appoint the local registrar who is to act as local registrar for the combined primary registration district. If the health commissioners fail to appoint the local registrar for the combined primary registration district, the director of health shall appoint the local registrar.
With the approval of the director of health, each local registrar shall appoint a deputy registrar who, in case of the absence, illness, or disability of the local registrar, shall act in the local registrar's stead. Acceptance of appointment as deputy registrar shall be in writing and shall be filed with the director. No funeral director or embalmer shall serve either as a local registrar or as a deputy registrar.
In a city registration district, all the records of vital statistics shall be kept in the office of the board of health of the city health district. In a general health district, all the records of vital statistics shall be kept at the office of the board of health of such district.
R.C. §3705.05