Hi, Richard. My name is ***** ***** I will be happy to help you.
You will not need to file WI state tax return if you are nonresident and you don't have more than 2K from WI sources.
You are a nonresident if you are not domiciled in Wisconsin for any part of the taxable year.
What is your Domicile - Your domicile is the permanent legal home you intend to use for an indefinite or unlimited period, and to which, when absent, you intend to return. It is not always where you presently live. You can be physically present or residing in one state but maintain a domicile in another. "Domicile" is often referred to as "legal residence." You can have only one domicile at a time. Your domicile, once established, is never changed unless all three of the following occur or exist:
• You specifically intend to abandon your old domicile and take actions that show that intent,
• You intend to acquire a new domicile and take actions that show that intent, and
• You are physically present in the new domicile.
Things that determine your domicile are home ownership, residence of your closest family members, obvious things like your driver's license, ID, where are you registered to vote and finally where you spend most of he time.
It looks like your domicile will still be TN, not WI. Which means, unless you have income from WI sources over 2K, you will not need to file WI tax return.
Income from WI sources is: job, rental income, sale of RE located in WI, business located in WI, WI Lottery, WI casino winnings, or any other WI based contracts or activity.
Here's WI tax publication that describes all in more details: https://www.revenue.wi.gov/pubs/pb122.pdf
Let me know if you have any questions.