As @Hal_Al stated in an earlier response, you must file two state tax returns: a non-resident Illinois state tax return and a resident Ohio state tax return. The issue for state tax purposes is where you live and where you work. The location of your employer's home office is irrelevant.
Illinois can tax the income you earn from work you carry out within Illinois; Ohio can tax all your income, including that from Illinois. You will be able to claim an "other state credit" on your Ohio return for the tax you pay to Illinois. The credit prevents double taxation of the same income.
With TurboTax, you must complete the non-resident state return before you do your home state return, so that the program can calculate and apply the credit.
If you worked both in and out of Illinois during the tax year, then you must calculate the Illinois portion of your income if your employer does not do that for you.
Going forward, if you continue to work in Illinois and your employer does not withhold Illinois income tax from your pay, then you must make quarterly estimated tax payments to Illinois. You can make those payments (if necessary) online here:
https://tax.illinois.gov/individuals/pay.html
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
