You can indicate in TurboTax that you lived in more than one state for 2017. On your federal return, you will enter all of your income earned (from both states). Then TurboTax will recognize and work with you that you need to file a part-year resident return for California for the portion of the year you lived there. Washington does not have state income tax, so you will only need to file your federal and part-year CA resident returns.
Here is more information on filing a part-year state return: