My husband is in the Navy and had a car registered in Va where he was stationed at the beginning of 2016. I had to re-register the car in TN our state of residence

The answer to your question is that there is no tax deduction directly available for vehicle registration fees on a personal tax return.  However, if you live in a state that imposes an excise tax amount, and that is part of the vehicle registration process, then the excise tax portion can be deducted, but not the whole amount of the cost of registration.  (This is what you see in the TurboTax program, under the "Car Registration Fees" deductions tab.)

The legal reasoning for the excise tax deduction is as follows.  The IRS only allows that portion of a state registration fee that is based on the value of the vehicle to be included toward a taxpayer's itemized deductions.  Any flat fee portion of the registration, or a fee based on any factor other than value, doesn't count.  This is why there are some 20+ states whose residents can potentially benefit from the deduction; but the remainder cannot:  their states do not charge vehicle registration fees by value, and instead charge flat fees only.

There is a list of these qualifying states built-into the TurboTax software.  A graphical image of this chart of states is also shown in one of the screen-capture image at the bottom of this answer (simply click to enlarge).

If your state is on the list, then you can enter the vehicle excise tax amount in TurboTax.  Unfortunately, neither Tennessee nor Virginia are on that list.  As such, these states don't charge a registration fee based on value.

We are sorry to have to inform you of that; but at least now you know the facts, and the reasoning behind the (potential) tax deduction.

Thank you for asking this important question.