Ohio Rev. Code § 3109.03: Equality of parental rights and responsibilities.

When husband and wife are living separate and apart from each other, or are divorced, and the question as to the parental rights and responsibilities for the care of their children and the place of residence and legal custodian of their children is brought before a court of competent jurisdiction, they shall stand upon an equality as to the parental rights and responsibilities for the care of their children and the place of residence and legal custodian of their children, so far as parenthood is involved.