If you and him really believe that you're broken up for good, then i think you should give it back to him, because there's no reason for you to have it, if there's no reason for you to go there anymore.
Give it back right away. It could cause issues later on if you still have it. If you decide to work things out you can get it back. You'll probably want to get your bed but you really shouldn't let yourself in without him knowing