You will find on this website: Learn about tax treatment of unemployment compensation ..., that Massachusetts does continue to tax the unemployment even after you have moved to another state. Since Louisiana can tax this income also, you should receive a credit on your Louisiana return for the taxes you pay to Massachusetts on the income taxed by both states. But that credit could be $0, especially if either of the two states have followed the Federal tax return's provision of exempting up to $10,200 of unemployment benefits.
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