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Could you please provide more background information of the circumstances which are behind your question?
Thank you. No, there is not a privacy law that prevents the landlord from doing that. Is it against the law? No. Is it unprofessional? Yes.
Now, if the landlord is telling others that you smoke pot and if you don't, then you can demand that your landlord take the statement back. If the landlord doesn't, then you can meet with a local attorney to review your options to sue your landlord for slander. Accusing someone of a crime, when no crime was committed is slander.
Good luck and best wishes! I hope that you find this information to be helpful and this answer to be ACCEPTable!
Attorney
Michigan lawyer who explains basic criminal, consumer, and contract-related matters.