Do you need to file state taxes for TN? My company did not take out state taxes on my w2.

Tennessee doesn't have a state income tax so your W-2 is correct. 

Tennessee has a "hall tax" -- that is, a 6% tax on interest and dividends, which is specifically allowed by the state constitution. Tennessee also has a 7% sales tax. See These States Don't have Income Tax for additional information.

No. TN does not have a regular income tax. 

TN does tax  interest and dividend income, only, starting at $1,250 ($2,500 if married filing jointly).