In almost all cases, the answer is no. This is an old myth.

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The questions on the Ohio State Medical Board's licensing application and renewal application focus on impairment, not diagnosis and treatment. In other words, you do not have to report that you are in treatment. You only have to report if you are currently experiencing impairment that impedes your ability to practice medicine safely, AND for which you are NOT receiving treatment. 

 

See also the Federation of State Medical Boards’ Policy on Physician Impairment.