Adding Your Name to Your Child's Birth Certificate Is NOT Enough
Were you married to your same-sex partner when your child was born? If so, the State of Ohio will list both of you on your child's birth certificate. Unfortunately, that is NOT enough! A birth certificate is an administrative document, not a court order. The Social Security Administration, some Ohio courts, and other states may not consider both of you to be the legal parents of your child.
Did you know that the Ohio Statutes concerning parentage still refer only to a “father” and “mother”? That is problematic for two mothers or two fathers. And yes, the U.S. Supreme Court legalized gay marriage in 2015, but the Court did not rule that states must also recognize the legal rights of LGBTQ parents. That's why I strongly recommend that married same-sex couples obtain a court order for the "other" (non-biological or non-adoptive) parent.
Your child will also benefit from having a court order which establishes full legal rights for both of her parents. You can file a "Petition to Establish Parentage" in Juvenile Court if you were married at the time your child was born. If you married after your child was born, you can file a Petition for Adoption in Probate Court. The end result is the same: Your child will have two legal parents for her entire life, and both you and your spouse will have full legal rights to your child. A win-win!