Since you lived in both California and DC last year, file a Part Year Resident State Return to both states.
Report only the income earned/taxes paid to that state on the Part Year Resident return.
You can use the amounts already shown on your W-2 for this, or you can make manual adjustments for the month that belongs to CA but was reported under DC.
Click this link for more info on How to file a Part-Year Resident Return.
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