No. Tennessee does not have a state income tax since they do not tax individuals' earned income, so you are not required to file an individual Tennessee state tax return.
Tennessee residents are only taxed on dividend and investment income (if dividend and investment income exceeds preset limits). If you did not have dividend or investment income, then this is a situation where you would not need to file a Tennessee state tax return.
You will only need to file a Tennessee state tax return if you received more than $1,250 in taxable interest and dividends ($2,500 if you are married filing jointly).
The Tennessee income tax does not apply to salaries and wages, but most income from stocks, bonds and notes receivable is taxable at a flat rate of 6%. The first $1,250 in taxable income received by a single filer is exempt.
See the Tennessee Department of Revenue website at: