The answer depends on your circumstances.
The state's department of taxation says the following for non-residents like yourself:
"a nonresident, you must file Form IL-1040 and Schedule NR if
-
- you earned enough taxable income from Illinois sources to have a tax liability (i.e., your Illinois base income from Schedule NR, Step 5, Line 46, is greater than your Illinois exemption allowance on Schedule NR, Step 5, Line 50), or
- you want a refund of any Illinois Income Tax withheld in error. You must attach a letter of explanation from your employer.
NOTE: If you are a nonresident and your only income in Illinois is from one or more partnerships, S corporations, or trusts that withheld enough Illinois Income Tax to pay your liability, you are not required to file a Form IL-1040." See Illinois
Revenue website.
Note that the rental property's income is Illinois source income, which will be needed when determining your income for Illinois filing purposes.
Note that if you have a loss from the rental property but expect that you may have a profit in the future, that you may want to file the Illinois return - even though you are not required to - in order to show the carryover loss for a future year.