The 23 year old boyfriend and/or the parents of the 16 year old need to consult with an OH attorney. I suspect that the boyfriend and perhaps the child's parents might be guilty of contributing to the delinquency of a minor. If they really need to live together, it would be best for them to be married, unless there is an OH statute which restricts her marrying at that age.
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I am not an OH lawyer, but a quick Google search tells me that due to the age difference, a sexual relationship is illegal. But you might want to consult a local lawyer. Candidly, the age difference here is pretty shocking. It is also shocking that her mom would consent.
This post is for information purposes only and does not constitute legal advice, nor does it establish an attorney client relationship with Mr. Cassara.