My permanent resident at Ohio and my earning from to Illinois. I commute M-Thu and have rent apt. in to Illinois . Do i have to pay resident tax for both state?

Yes & no. You have to FILE a return in both states. You  will file a non resident IL return and pay tax on your IL income. You will file a resident OH return and calculate tax on all your income. But, OH will give you a credit for what you pay IL; so there is no double taxation.

No - If you maintain your permanent residency in OH, then your residency in IL would only be on a temporary basis (even if you are there for work all year). Therefore, you would claim OH as your resident state and IL as your nonresident state.

Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)

https://ttlc.intuit.com/replies/3300797

I'm in the same boat, but I've further question, I pay Ohio local taxes quarterly as a resident, can I claim the credit for local taxes paid to Ohio county,  on my IL- state tax return as well?

No. IL Schedule CR does allow a credit for local tax paid in another state; but that is only for IL residents.

"A nonresident may not take a credit on Illinois Schedule CR".
Reference: Instructions for Schedule  CR (<a rel="nofollow" target="_blank" href="http://www.revenue.state.il.us/taxforms/IncmCurrentYear/Individual/IL-1040-Schedule-CR-Instr.pdf">http://www.revenue.state.il.us/taxforms/IncmCurrentYear/Individual/IL-1040-Schedule-CR-Instr.pdf</a>)

PS. There are no "County" income taxes in Ohio. What you are paying quarterly is either City or School District Income Tax (or both).

Above comment revised

Thanks for your comments. Yes, I pay city income tax.

I'm planning to put money in OH-529 plan ( I won't get the tax deduction on IL-529 / I'm not eligible since I'm non-resident). But putting money in OH-529 will just reduce my OH state tax liability, but as I've to pay IL state taxes, I'll be getting the tax credit of the OH state tax, so in total I won't get the tax deduction on 529 amount I'll be putting in OH-529 plan. Am I correct?

Yes. Since the IL tax is greater than the OH tax, you already get a 100% Ohio credit.  That is, your OH tax is already zero. Additional deductions on the Ohio return (not allowed on the IL return) will do you no good.