State tax filing

you don't. as to your wife's income you only pay taxes on it in Iowa. there is no IL-W-5-NR in the Illinois state return. that is a form you either get online - see link -  or her employer. 

https://www2.illinois.gov/rev/forms/withholding/Documents/currentyear/il-w-5-nr.pdf 

 

if Illinois taxes were withheld you'll have to file in Illinois to get them back.

you need to file form IL-1040 and schedule NR which is not yet available as of 2-1-2021.

you may need to override line 5 on form NR which will require you to mail in the Illinois return. 

per prior year NR instructions

schedule NR Line 5: Wages, salaries, tips, etc.
Enter the amount shown as Illinois wages on the Illinois copy of the
W-2 forms you received while you were a nonresident.
Do not include any Illinois wages you received while
you were a resident of Iowa, Kentucky, Michigan, or Wisconsin.