Tennessee does not impose a state income tax, other than the so-called "Hall Tax" on interest and dividend income.
Generally, if you are a person moved into or out of Tennessee, you only need to file the Tennessee Hall Tax return if your taxable interest and dividend income, during the period of Tennessee residency, exceeded $1,250 ($2,500 if married filing jointly) during the tax year.
If you don't need to file a Tennessee state tax return, and TurboTax has generated one for you, you can delete a state return in TurboTax Online, as long as you haven't paid for it yet (or registered in a free version).
Please see the following TurboTax FAQ, "How do I delete my state return in TurboTax Online?":
For more information about Tennessee's Hall Tax, please see the following Hall Income Tax Return guide from the Tennessee Department of Revenue: