Ohio Rev. Code § 3111.58
If an administrative order determining the existence or nonexistence of a parent and child relationship includes a finding that the child's father is a man other than the man named in the child's birth record as the father or is otherwise at variance with the child's birth record, the agency that made the determination shall notify the department of health of the determination as soon as any period for objection to the determination provided for in former section 3111.21 or 3111.22 or section 3111.49 of the Revised Code has elapsed.
On receipt of notice under this section or notice from an agency of another state with authority to make paternity determinations that has made a determination of the existence or nonexistence of a parent and child relationship, the department of health shall prepare a new birth record consistent with the agency's determination and substitute the new record for the original birth record.
R.C. § 3111.58