Here's a plugin from Cristian Bote that allows you to create transitions between two Phaser states:
"The plugin basically overrides the create state method, so you could keep you're code the same, and just add transition configs where you see fit.
game.state.start('playState', [outTransition, [inTransition]], clearWorld, clearCache, parameters);Notice the 2 optional params, that are transition config instances. There are several available by default and you can easily add your own nice transitions as well."