Nine states — Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington and Wyoming — have no state income taxes.

As your state Texas has no state income tax, it is not in the drop down menu of Box 15 of form W-2. Just leave boxes 15 and 16 blank even if TX is listed in box 15 and box 16 is filled with an amount on your form W-2.

Even though Tennessee does not have a state tax it is requiring me to answer, but I can not answer because TN does not come up under the drop down list

Tennessee has no income tax on salaries and wages, so box 17 should be empty, leave box 15,16 and 17 blank. If there is an amount in box 17 then TurboTax will ask you to enter the state information in box 15 and 16, in that case, contact your employer for a corrected W-2.