Ohio Rev. Code § 2111.08
The wife and husband are the joint natural guardians of their minor children and are equally charged with their care, nurture, welfare, and education and the care and management of their estates. The wife and husband have equal powers, rights, and duties and neither parent has any right paramount to the right of the other concerning the parental rights and responsibilities for the care of the minor or the right to be the residential parent and legal custodian of the minor, the control of the services or the earnings of such minor, or any other matter affecting the minor; provided that if either parent, to the exclusion of the other, is maintaining and supporting the child, that parent shall have the paramount right to control the services and earnings of the child. Neither parent shall forcibly take a child from the guardianship of the parent who is the residential parent and legal custodian of the child.
If the wife and husband live apart, the court may award the guardianship of a minor to either parent, and the state in which the parent who is the residential parent and legal custodian or who otherwise has the lawful custody of the minor resides has jurisdiction to determine questions concerning the minor's guardianship.
R.C. §2111.08