I am sole custodian mom; father has no visitation, or child support in place. Can I move to another state without written notification to the father?

If the father has gone through the paternity and legitimation process, their is a duty to provide the other party 30 days notice of any change of address. If he has not followed that process, it is unlikely that you are under any obligation to notify him. The information provided is illustrative in nature and not intended to be legal advice. Only with a full understanding of all the facts can appropriate legal advice be given. You are strongly encouraged to schedule a consultation with an attorney to fully discuss your matter.