If my roommate is not on the lease in current apartment, but he refuses to move, am I legally responsible for my roommate?

You have allowed an unapproved individual to reside with you. Technically you are responsible to ensure he moves when you do. You can serve him with a Notice to Quit and then follow up with an action for eviction. If you move and he does not, the apartment complex will do that. They can also sue you to recover the costs of evicting him. The best thing to do is try to have the apartment complex add him to the lease so that he remains responsible when you move.