Tennessee does not impose an income tax, except for a so-called "Hall" income tax on interest and dividends:
You only need to file a return for the Tennessee Hall tax on interest and dividends, at a rate of 5%, if you are a person whose legal domicile is in Tennessee, and whose taxable interest and dividend income exceeded $1,250 ($2,500 if married filing jointly) during the tax year.
For more information, please see the following guidance from the Tennessee Department of Revenue on the Hall tax for the 2016 tax year, below:
https://www.tn.gov/assets/entities/revenue/attachments/indincguide.pdf
If you find that you do not have a requirement to file a Tennessee return, and TurboTax has generated a Tennessee return 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?":
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