It depends. If you live in New York, all of your income is reported to New York. If you live in Kentucky, all of your income is reported to Kentucky. If you live in Kentucky, your income from New York is reportable to New York if you were either physically present in New York or telecommuted from home for a New York company.
If in any case you must report income earned in another state to that state, your resident state will provide you with a credit for the tax you pay on the income earned in that state. It is recommended to prepare the nonresident return first so that the credit for those taxes transfer over to the resident state return.
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