Imagine you are searching for a new place in New York, and you find the perfect place. It doesn't allow pets, but that's no worry -- you don't have one. For a few years, you live happily in your apartment.
Then, one day, you suffer a medical setback. It could be that your vision dramatically decreases; or you begin suffering from clinical depression. In an attempt to curb the effects (or to directly help you get through the day), you want to get a dog. With a disability or a serious mental or physical health condition, you are allowed to have a dog with you in your rented apartment -- even if the rules forbid it.
However, for those people with less serious mental or physical complications (but complications that are still debilitating and impactful), the rules and their application are a bit more ambiguous. In order for someone to be given permission to have a dog in a no-pet building, the tenant must prove two things:
Whatever disability or condition that the person is living with, it must fit within the medical and legal definition of that condition. So, for example, seasonal depression or recently breaking up with your boyfriend or girlfriend does not mean you fit within the medical guidelines of "depression." Proving your disability or condition to your landlord or co-op board is a requirement.
You must prove that having a dog will be medically beneficial.
It can be difficult to fulfill these requirements, and a tenant who wants (or needs) a dog to help with his or her medical condition should consult an attorney to craft the best possible case to make to their landlord.
Source: New York Times, "Do You Have a Doctor's Note? Getting a Dog Into a No-Pet Building," Susan Stellin, Sept. 27, 2013