Dividends are income you receive. The fact that you reinvest them does not change the fact the you received extra money, even if it was invested for you. You will receive a 1099-DIV for any dividends that needs to be reported on your tax returns. Each state will have whatever share was earned while in that state. You can check your dividend distribution dates to determine which state you lived in.
The caveat being dividends from IRA/ pension/ retirement type plans would not be taxable. A regular mutual fund would be.
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