How Do I enter non paid preparer information for Ohio in Turbo tax

You can't, and you don't. TurboTax is for self-preparing a tax return. It is intentionally designed so that nothing can be entered in the Paid Preparer Use Only box, weather the preparer is paid or not. TurboTax has separate products for use by EA's CPA's and other entities that prepare taxes on behalf of others. One I know of is called Lacerte'. I forgot the name of the other one.

I know there's a line on the form for that.  But I don't see where it can be added in TurboTax, and I suspect that it can't be done.  You may have to print your form, add it manually and then mail your OH tax return.

For the federal return, you add the "Third Party Designee", in the forms mode (not available online), on the 1040 worksheet.  But that does not transfer to the Ohio form.