I started to say 'both parties can move wherever they want', but thought about it some more. Is the respondent still in state? If so, then I'd say that the petitioner can move.
OTOH, if the respondent is out of state and then the petitioner moves out of state, then that state may no longer have jurisdiction - which would confuse things quite a bit. However, I'm not sure if you have to be in state at the time of filing or the date of the judgment - someone else will have to answer that.