The Ohio Department of Health's vital records webpage shows a few ways you can get the death certificate, certified or not. If you're not looking for the entire certificate, just some information, you can do it without costing anything, other than the time it takes to look it up. The Ohio libraries archives has information only, not the certificate, which you can view freely for deaths between 1913-1944 1954-1963 and more.
Here's a look at the open data: Last name, fist name, date of death, County, Vol. number Cert. number (State Death Certificate)
Feb 26, 2016