State tax filing

It depends. Let's start with residency:

Your son lived in IN but if he was your dependent, your address is his permanent home while in school. If you also live in IN, then part year is correct. His driver's license, voting, and car tag tell his story. He may not be a dependent.

For IN 

• tax can be based on where you work and /or where you live. See DOR: Individual Income County Tax Rates by Year. Each location has its own rules.
• Nonresident or part- year resident

For IL

• Has he established his new home or is this a job that may not pan out, or transitional. Did he get the new license, rent a place to live and establishing new social connections?
• Nonresident passing through, unsure if staying or part-year resident.

If he is filing 2 part year returns, then only the income associated with that state is reported. IN will give a refund of the over withholding and IL will need to be paid.