Ohio county probate courts have kept marriage records from the date of the county's formation. There is no statewide index to marriage records before September 7, 1949.
Special Collections and Archives has the following marriage records:
Contact the county probate court for marriage records not available in Special Collection & Archives.
To obtain a copy of a marriage record after September 7, 1949, contact the probate court of where the marriage occurred.
The Ohio Department of Health maintains a statewide index to marriage records for all Ohio counties from September 7, 1949, to the present.
An index to Ohio marriage certificates for 1789-2013 is available through FamilySearch