@Bimaculatis thank you for participating in our event today.
That is correct WI and MI are reciprocal states which implies that you can live in one state and work in the other and only have tax withholding for your resident state. In your case MI is/was the resident state and WI is the state you are working in.
The state of Wisconsin will consider you a resident for tax purposes if you maintain domicile in WI. A "domicile" is a person's true, fixed, and permanent home where a person intends to remain permanently and indefinitely and to which a person has the intention of returning, whenever absent. It is often referred to as "legal residence." A person may be physically present, working or living in one place but maintain a domicile in another. A person has only one domicile at any point in time.
If you are still maintaining a home in MI and plan to move back to MI after your onsite work is completed in WI, then you are still a resident of MI and you can have taxes taken out for MI and file as a resident of MI. The information you provided here is not enough for me to make a determination about your domicile.
I have included a couple of links here for more information.
Legal Residence/Domicile of Wisconsin
What is a state reciprocal agreement?
