I just came across this well organized summary of Ohio bicycling laws, which was compiled earlier this year by the recently deceased Cal Kirchick, an avid cyclist and attorney. It is a must read for anyone who rides the roads of Ohio. (Scroll down a bit on the page after clicking on the above link.)
It is definitely a must read for the gentleman we encountered today on our ride who insisted that we should ride single file on the four-lane Shaker Blvd. because, according to him, Westlake forces cyclists to ride single file (which is likely an invalid law) and in bike lanes when available (which is even more likely an invalid law). Sorry Dorothy, but you're not in Westlake anymore.