Illinois Resident with Wisconsin Real Estate Sale

My wife and I file jointly in Illinois as full-time, retired residents.

 

My wife inherited real estate in Wisconsin and sold it six months later.

 

Do we need to file a Wisconsin tax return to avoid a matching notice on the 1099-S from the Wisconsin closing?

 

Since this is a short-term capital gain—not W-2 income—how do I fill out the Illinois and Wisconsin returns?  Does the answer change if it is a capital loss and it is more than offset by other (Illinois) capital gains?

 

Thank you for reading this.