Did you know you can do this online now?
http://www.huntercourse.com/
I noticed that Ohio is not on that list, but we do have our own online course. But even if you take the online course in Ohio you still need to take the exam at either a class or the DOW to become certified.
http://wildlife.ohiodnr.gov/education-and-outdoor-discovery/hunter-and-trapper-education
Jerry
Arizona is not on the list but does have an on-line course. Out here you must also have a range day with rifle and shotgun.
I dont know how all the listed ones work, I only read Wisconsin's but they require one field day also.