The answer to your question depends not so much on where your wife earns her other income, but rather what state is her home state of residency (i.e., legal "domicile" in the colorful language of the tax law).
If she lives and works in another state than you do, then she would (probably) not be subject to the Tennessee Hall tax. However, merely having a job in another state (while still being a Tennessee resident) does not exempt someone from being subject to the Hall tax. It is certainly possible for spouses to live apart, for instance, and to have different state residencies.
For the sake of example, you could be a resident of Tennessee, and your spouse a resident of Kentucky (if she maintained a separate home and job there, for instance, voted in Kentucky, had a Kentucky drivers license, etc.). If that were true, then she could escape the Tennessee Hall tax.
But if someone is a bone fide resident of Tennessee, that person is potentially liable for the Hall tax, if their interest and dividend income is greater than $1,250 per year.
For some additional information on this unique Tennessee state tax, please read another (longer) post that I recently wrote about this very subject. The Hall tax is discussed there (link below) as well as some exceptions to it:
https://ttlc.intuit.com/questions/3679043
Finally, here is a link to the definitive Tennessee Department of Revenue official statement on the Hall tax (6 pages):
http://www.tn.gov/assets/entities/revenue/attachments/indincguide.pdf
The requirements of who must pay the tax, and who does not have to pay, are detailed therein along with multiple examples.
In your wife's instance, though, this really becomes a question of her Tennessee residency (domicile). That's a determination you'll need to make based on her specific circumstances.
Thank you for asking this question.
