If my divorce was filed in one state but I've moved to another, can the case be closed out in the state in which it was filed and then refiled where I live now?

If both parties agree to dismiss the case in the state it was originally filed and you meet the 6 month residency requirement for the State of Florida,you can refile it here.  However, if you have children in the other State, and you are dealing with where the children are going to reside as an issue in the divorce, you will have to go where the children are.