From everything I've read, you actually need to be an Ohio resident to access the Cleveland library.
There are a few other libraries that will give an out of state resident a card for a fee. I know the Salt Lake County library does this.
You can check out libraries in the wiki here at MobileReads:
https://wiki.mobileread.com/wiki/EBook_Lending_Libraries
Also, checkout the search page provided by Overdrive (company that supplies most of the libraries with their e-books and audio books).
http://search.overdrive.com/
dordale