My W2 has 2 states listed under line 15, MN and WI. I live in WI, but the facility that I work at is in MN. Can I claim this W2 for WI?

Yes.  Enter the W2 as it is written.  After entering the W2 info in the federal interview you need to work the MN nonresident return before WI.  

MN will tax only the income earned in MN shown on W2 box 16 for the MN line. You will allocate only the income that belongs to MN to MN in the MN state interview.  The W2 entry prepopulates the wages in the MN interview but you can change if it is not correct for any reason.  

 WI however as your resident state taxes on all income from all states including the income in box 16 for the WI line.  WI however does offer a credit for taxes paid to another state to mitigate the double taxation.  When you get to the "Credits" section in the WI interview be sure to select "Yes" you want to work the credit.  It will be prepopulated with the MN information from the MN return you worked first.  You can verify/update as needed.