TN has no state income tax, it is not in the drop down menu of Box 15 of form W-2. Just leave boxes 15-17 Blank, no spaces.
Several states do not have a state income tax. So these states will not show up in certain drop down lists. Leave boxes 15, 16, and 17 blank when you enter a W-2 for these states.
Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington and Wyoming
Some software produces that print W-2s and 1099s automatically populate the state boxes with state codes, even when it doesn't make any sense.
For example, Tennessee doesn't have a state income tax, so there is no need to enter boxes 15-17 on your W-2.
If there is no entry in box 17, then just make no entry in box 15 (or 16 for that matter).