It depends on whether these were permanent or temporary residencies.
If they were permanent residencies, but something came up and you decided to move, then you would be a part-year resident of California and a part-year resident of Washington D.C.
File part-year tax returns for both states.
You said you spent three months in CA and five months in DC, so you would also be a part-year resident of someplace else for the other four months.
If one of your stays was temporary, such as attending school or taking a limited job assignment, and you maintained a permanent home in CA or DC, then you would be a full-year resident of your permanent state and a non-resident of the other state.
You would file a full-year resident return for your permanent state and a non-resident return for your temporary state. Your permanent state will give you credit for taxes paid to your temporary state.
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