Unfortunately no. What happens is that you get a MN state tax credit for taxes paid to WI.
You will need to
file as non-resident for WI (for your WI source income only (your wages)). You will also
need to file a MN resident state tax return (for all income from all sources
including MN). You will get a state tax credit in MN for the WI state taxes the
your paid on your nonresident WI state tax return.
You will want to
file your non-resident WI state tax return first. You will then take a tax
credit from your non-resident WI return on your resident MN state tax return.
(Please note that you will only get a tax credit for your WI taxes up to the
amount of MN taxes that would have been paid if the income was earned in
MN).
Just follow the
TurboTax guide when working on your states (remembering to do your non-resident
state return first) and TurboTax will do all the calculations and credits to
your resident states return
Here is additional
information about filing in multiple states
https://ttlc.intuit.com/questions/1900021-when-would-i-have-to-file-returns-in-more-than-one-state
