The income you receive should be allocated to the state in which you were living when you received it for things like dividends and capital gains.
For interest bearing accounts, it wouldn't necessarily be when you actually get your hands on the money rather you should use the percentage of the year since that was being earned daily.
So in your situation, I suggest you separate the interest if possible. If that is not possible, I would allocate the full 1,000 to Michigan since you were living there when you received the income.
Here is a link to another TurboTax answer to this type of question.
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