Your husband can adopt your son here in NY assuming you meet the residency requirement. The biological father can sign a consent in Kentucky and as long as it is properly notarized the courts here will accept it.
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This is an example of a situation where a lawyer's skill is needed to coordinate a court case. There is the need to file the appropriate family court petition here and to get the necessary releases in the other state. Then, the case can com together.
This procedure is complex and detailed enough to warrant retaining an attorney, and you should contact one now, while you are formulating your plans.
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