If you don't have moisture on the floor, or coming through your walls, a de-humidifier might do the trick in reducing the amount of humidity in the air.  

If humidity, then you want to gear towards De Humidifiers versus A/C. 

Running the exhaust fan when showering, not running humidifiers in the property, cleaning bathrooms regularly and reporting mold upon first sight.When I first started my lease was three pages and it is now 15 pages.

Drip leg missing5.6.A Vent pipe repair 5.6.B vent pipe for gas furnace 5.0.C humidifier at utility room gas furnace not working6.0.A.2 needs plumber to look at sewer connection 6.1.A.2 plumbing leaks 6.2.A.3 existing piping for T&P valve on water heater fails to extend down 6 in.

Replacement is the issue.AdditionsBedroom Bathroom Deck Garage Porch PatioHeating & Air ConditioningHeating system Central air conditioning Furnace Duct work Central humidifier Filtration systemLawn & GroundsLandscaping Driveway Walkway Fence Retaining wall Sprinkler system Swimming pool MiscellaneousStorm windows, doors New roof Central vacuum Wiring upgrades Satellite dish Security systemPlumbingSeptic system Water heater Soft water system Filtration system [b]InteriorImprovements[/b]Built-in appliances Kitchen modernization Flooring Wall-to-wall carpeting InsulationAttic Walls Floors Pipes and duct workThis is not a finished list this is just an example.

However, my tenant notified me that there is water leaking from the humidifier and drain so there is a small puddle underneath the furnace.

If this occurs, quickly dry carpets (if carpets stay wet, notify the landlord).Use the kitchen fans when cooking.Don't run the shower to humidify you home.Avoid using humidifiers unless there is a medical reason to use one.Ensure good air environment in your home to prevent condensation on cold surfaces open windows when possible don't block supply and return registers with furniture keep a few inches of space between furniture and walls don't let parts of your home get very cold (such as closets against exterior walls)Watch what you put down drains to avoid clogging and over-flowsWhen moisture problems do occur, it is critical to quickly report the cause of moisture and to dry affected areas.

Humidifiers and fans too?

Use exhaust fans or open the windows in the kitchen and bathroom when cooking and showering and for awhile afterward.)Use air conditioners and de-humidifiers when needed.Unfortunately, @Bruce Chang, whether there is or isn't a mold hazard in the home, the tenant may perceive there is.

@Bryan Neal, @Beth L. and @Lee Liu ,If these things really are no more harmful than a humidifier, I'd probably take a chance and let a tenant use.