Hi klnimada!
You will need to account for the income earned in each state separately. If the intent is to remain in Washington, you will need to complete two state returns. Washington being the resident state and New York being the non resident state. Any taxes that you are required to pay in the non-residential state will be used as a credit on the resident tax return.
If you are moving to New York, again two state returns will be required but both states are considered part year and you'd pay taxes separately based on the amount of income earned in each state as no credit is given in that case.
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