No, you only need to report the dividend income received while a TN resident.
When completing the TN state interview you will arrive at a page titled "Tennessee Dividend Summary." You will "Edit" the line. You will put in the amount of dividends that are non-taxable to TN in the "non-taxable" box.
Here is a link confirming how TN handles the Hall tax for part-year residents.
Also, note the Hall Tax is repealed as of 1 January 2021. Here is the confirmation link.
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