Ohio Rev. Code § 124.35: Refusal to testify constitutes unfitness.

In any hearing on the question of fitness and continued employment of any person holding a position, job, or office under the authority of this state, the fact that he, being called before a duly authorized tribunal, or in an investigation under authority of law, refuses to testify concerning his membership in an organization which advocates overthrow of the government of the United States or of this state, by force, violence or other unlawful means on the ground that his answers might tend to incriminate him, shall constitute unfitness of such person for holding such position, job or office.