In the course of developing my workshop on Naturalization and Alien Registration for the Genealogical Committee of the Western Reserve Historical Society (details here), I discovered that the WayBack Machine provides access to the Naturalization Records database that was available on the Internet at one time.
Presently, the website is infected with some sort of virus, and–at least on my Google Chrome browser–there is a warning against accessing this website.
I have heard through the grapevine that this website eventually will be fixed and made available to the public again–perhaps later this month (April, 2014).
In the meantime, if you want to “root” around in the Cuyahoga Naturalizations database, go here:
When you “see” the record of backups created by the WayBack Machine, click on one of the backups (e.g. in 2009) and you will have access to the database.