Can an employer in the state of Ohio give an employee a bad reference? Is there anyway to find out if they are?

Depends on what you mean by bad. If it's along the lines of a potential employer asked if you are punctual and your previous employer admitted that you were late to work every other day and that's true, it's bad for you but since it's true it's legal. If you mean s/he was spreading malicious slander, no that is not legal. I have no idea how you would go about finding out what was said but maybe someone else will come along for that part.
Ohio Attorney General Richard Cordray Blog Archive Guidelines for Giving Employment References (http://speakoutohio.gov/employmentlaw/guidelines-for-giving-employment-references/)