I live in Florida which is very humid and mildew is a common occurrence. We actually have the tenants sign a mold addendum that explains how they are responsible to keep mildew or mold at bay by running exhaust vents when showering, treating visable mildew in window sills and bathrooms with bleach, cleaning the AC drainline, running AC when humidity is high ect...
My first thought would be to perform a walk through and see if they can show you what they think is the source of the smell or mold. It could be as simple as dirty laundry in a closet or a smelly drain. A walk through inspection could allow you to rule out alot of tenant related issues of false mold. Most types of toxic mold develop from a water or moisture source. If there is a leak or problem that you can identify it would be less expensive to remediate versus paying for inconclusive mold testing.
When a tenant complains of mold and complains that it is unsafe we always offer them the right to vacate, should they choose to remain they would have to sign a hold harmless agreement. we do always inspect and see if we can determine that the house may or may not have mold. Most of the time in my experience it is just a false alarm and tenants are looking for an excuse to live rent free or vacate without penalty.
