The Ohio Historical Society has created an online death certificate index for the years 1913 through 1944. While it does not provide the actual death certificate, it can be a helpful free genealogy resource if you know someone passed away in Ohio, but are not sure of the date or location.
The index is searchable by name. It appears that you can search by first or last name. If you are not sure on a surname spelling, you can try searching only the first name. Wildcards (?) and truncation (*) may be used in the search.
You can narrow your search by selecting a date span of 1913-1935 or 1936-1944. You can also select a county to narrow your search.
The search results screen will give you the individual's name, death date, county, the volume the certificate is found in and the death certificate number.
If you find the individual you are searching for and want a copy of the actual certificate, it is possible through the site for a fee. Just check the box to the right of the entry and then click on the button at the top of the page that says Step 1: Save Checked Records.
Then click on Step 2: Show Saved Records to go to a screen which will give you the option to purchase the death certificate online or to print an order form to be mailed. Currently there is a $7.00 fee per certificate ordered. Ohio residents will be charged tax.