Just because you are a nonresident or a part year resident, does not exclude you from paying income taxes to CA. There are hundreds of reasons why you wouldnt owe taxes to CA, as a nonresident or a part year resident, far too many to get into detail here on this board. But I assure you, nonresident or part year resident status does not exempt you from CA income tax.
For example, I have done returns for an NFL football coach who has to pay taxes in each state that his team plays a game.