Based on your facts, you were a nonresident of California. As a nonresident, you may have to file/pay on California source income (which is worked performed in California). See Filing requirements for the threshold.
You were a Part Year resident of Massachusetts and Washington state, so you would have to file a Part Year Massachusetts return, reporting your W2 amount. If you are required to file a California return, you will be able to claim a credit for the taxes paid to California on the same income taxed by Massachusetts.
In TurboTax, be sure to file your nonresident state first. See Multiple States—Where To File - TurboTax Tax Tips & Videos for more information.
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