If you and your spouse filed a joint federal income tax return, you generally MUST file a joint Ohio income tax return.
If you and your spouse filed separate federal income tax returns, you MUST file separate Ohio income tax returns.
So - in order to file separate returns - you need to file separate federal returns - however you may not amend your federal return changing the status from MFJ to MFS after due date of the return - therefore - you may not amend your OH state tax return at this time.
However you may file as a primary taxpayer and mark yourself as part-year residence. Than you would file schedule D to apportion your OH income.
I suggest to discuss this approach with your tax preparer.
Yes - you are correct - after return due date - that is April 15 - you may not amend your federal return from MFJ to MFS.
Because OH filing status should be the same as you used on the federal return - you may not file MFS on your OH return
However - even filing as MFJ - you may use OH schedule D. To do so - you should be listed as a taxpayer and your husband - as a spouse on the IT1040. In this case you will mark yourself as part-year resident and fill schedule D.