Ohio is an employment at will state, meaning you can be fired for any reason or for no reason at all. The exceptions to this rule are determined by whether you had promises ro an agreement with your employer to the contrary, or whether there is some form of discrimination involved. Given the nature of the rumors, if you feel that there is a a work environment related to sexual innuendo that ultimately led to your termination, you may have a case to pursue. You should speak with a good attorney who has a good working knowledge of Ohio employment law.
As I am licensed in Florida and Vermont, I cannot provide you with any specific legal advice as to Ohio state law. However, if you have provided information during the course of an investigation of a sexual harassment complaint, you cannot legally be fired or suffer an adverse job consequence for providing information or cooperating with the complainant. However, if you lied or deliberately withheld information,I think you legitimately could be fired for obstructing the investigation. Most employees, absent a binding contract to the contrary, are employees at will and can be let go for any reason as long as it does not violate an existing statute or public policy.