When it comes to birth records in Hardin Co. , OH you have several places to locate them depending on the time period that you are looking for the person. They are the Hardin County courthouse in Kenton and the archives in Bowling Green.
Birth records at the courthouse run from 1867 to present. This is where you would be able to get certified copies for this time period. As with all places of this type be patient with the staff and allow for some time with your search.
Finally the archives in Bowling Green has the birth records running from 1867-1908. They also have a copy of index to birth registration and corrections that runs from 1867-1986. All of these records are on microfilm.
Birth records give you excellent first hand information on time and place of birth. This is also the best source for parentage. Always make copies of these records for proof and verification.
Good luck in your search.