At the start of tenancy did you and the tenant sign a disclosure on mold and moisture hazards?
Did you give the tenant the EPA booklet "A Brief Guide To Mold, Moisture, and Your Home"? The booklet is an excellent resource and costs only 50 cents a copy. I give a copy to every tenant. A pdf of the booklet is available on line for free. Check it out. Also available in Spanish.
You have responsibility to provide a habitable dwelling. The tenant has responsibility to take action to prevent mold and mildew. Also to clean on a regular basis.
In Washington State, at the time the lease is signed, the landlord must provide the tenant with information provided or approved by the department of health about the health hazards associated with exposure to indoor mold. (see RCW §?59.18.060). That's law in Washington State. Any similar requirement in your state?
The Washington State Department of Health publishes a free two page form "Got Mold? Frequently Asked Questions About Mold" with signature/date lines for Landlord and Tenant. Quite informative and gives instructions on clean up. It's not state specific, so you may find it helpful.
All of our rental agreements include this Mold Warning Statement: "Mold may grow and exist in any structure where there is, or ever has been, a presence of moisture and a food source for mold to grow. Its presence may exist without the knowledge of the structure owner and may be concealed from the untrained observer. Some varieties of mold are toxic and may cause adverse reactions in certain individuals." With our signature, we attest that we have no knowledge of mold or moisture hazards in the unit. If there were, then we would have to disclose what we know.
You can be proactive from the get go and you must do what you can to prevent and remediate mold in your units. Good luck!