Would I need permission to move out of state with my children, given that I never married him and there is no custody agreement?

I have never married my children's father and there is no custody agreement. He does pay child support and if he gets medical insurance, he is court ordered to put them on it. He moved out of state at the beginning of May. I've been told that child support is a form of contact. My children's father has not contacted via text, call or message through social media (which he would do when he ran out of minutes) to speak with the children since he moved. I've heard from a mutual friend that he was back, but he has made no mention or contact to tell our kids. He just got a job, which I only know because of the child support deposit I got last Wednesday. Is child support a form of contact?