Hi. DO i have to file any forms for the state of ohio for 1099 Misc if i file with the IRS electronically? Or do they accept the federal electronic filing?

If you also E-filed your Ohio return, Ohio will accept the Federal filing.  

You do not have to mail anything to the state unless you are making a payment.

Yes, you (and all taxpayers) have to file a separate tax return for the state of Ohio. The fact that your income is on a 1099-Misc is not relevant to the filing requirement.