California Employment Law
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Subsection (b), above, suggests that if your crime is one of fraud, fiscal dishonesty, or theft, then this could be a disqualifying factor.
Unfortunately, there is no "bright-line" answer to your question. The best that I can do is to provide the law and regulations so that you can compare your conviction with the law and make your own determination.
I would also encourage you to contact the Respiratory Board and see if they are willing to provide you with any certainty concerning this issue. It would be a shame to do all the work only to be denied at the end of the road.
Hope this helps.