You are correct that you do not have to pay Tennessee state income taxes (Hall Tax), on your interest and dividend income, that was received during the portion of the year you were a nonresident of Tennessee.
In order to correctly calculate your Tennessee Hall Tax return, however, you will need to make some manual calculations, and then enter an "adjustment" to your Tennessee interest and dividend income.
We detail how to do that for another part-year Tennessee resident, in a more complete explanation, at the following clickable link:
https://ttlc.intuit.com/questions/3787652
Thank you for asking this important question.
