I found this publication to be really helpful regarding service dogs vs emotional support dogs, etc. It's for California, but it covers the basic laws from HUD and the ADA:
http://www.disabilityrightsca.org/pubs/548301.pdf
It includes this:
"...If you are seeking a reasonable accommodation for your service or emotional support animal for housing, a landlord or homeowner’s association may ask for documentation that you have a disability and that you have a disability-related need for the animal.
However, the landlord should not request documentation if your disability and your disability-related need for the service or support animal is obvious or the landlord otherwise should have known about the disability and need..."
It goes on to say you can't require details about their disability or their medical records. But, you can definitely require a health care professional put in writing that the tenant has a disability.
So, you can require a form to be filled out by her doctor or health care provider, or to get a letter from them on their letterhead. Some landlords actually give the tenant a form that must be filled out by the doctor, rather than just accept a letter the tenant provides.
She'll probably be able to get a doctor or shrink to say she'll benefit from having one, but as someone else mentioned, if there is some question about your "allowing" a dog, you can show that you never changed your pet policy. Being required to provide a reasonable accommodation is not the same thing.
