As far as I can remember The Ohio returns that I have done I have always finished by the deadline. But you are right they do not have a separate extension form. They do have form it40p that allows to make an extension payment. I wonder if this can be filed, e filed or paper filed, even if zero payment and accepted as a legitimate extension? Or can a copy of the federal extension be mailed directly to Ohio and accepted by them? Maybe Jim from Ohio or someone else from Ohio can answer this.