See if this previous answer helps you.
What this line of questioning is trying to figure out is what state returns you need to file. You usually file state returns in your domicile (where you permanently live) (taxed on your worldwide income) and also in other states that 1) you phyiscally worked in during the year or 2) that you own property (e.g. rent a house, sell a house) or a business in (only taxed on the amount of income from those states).
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