Can you move out of state with an on-going case involving CPS?

Depending if there is an open investigation or if the investigation has finished without charges pending. The safest bet is to call the case worker or supervisor to determine the status of the case.

If the case has criminal charges pending, that would be no. It is called fleeing to avoid prosecution. If you and your case worker have a Family Plan in place you must notify your case worker and quite possibly they will want you to set up an appointment with Family and Child Services in your new location.

Anytime you are involved with a state agency you should notify your case worker or supervisor when you have a change of address. People who move during an investigation or with a Plan in place without notifying the agency, can face criminal prosecution.