State tax filing

In the personal info section of TurboTax where it asks for your state of residence, there's a button to also indicate you were a resident of another state during the year. Make sure that box is checked and that you choose New Jersey. This should allow you to set your residency as part year resident for both states.

Next, make sure you choose No for the question that asks if you earned income in another state. If you did earn income in a state other than CA or NJ, choose yes and only include that state - not NJ.