“It’s not unreasonable for a landlord to make some additional inquiries about the case,” said Karen Copeland, a lawyer who has represented dozens of clients seeking such waivers.

Among them: a woman with lung cancer whose dog helped prevent her from smoking cigarettes (“It provided her with a distraction”); someone with Parkinson’s disease (“It was able to diminish his symptoms, like trembling”); and a recovering alcoholic (“The dog gave her social things to do — she could go to a dog park and make friends”).

Ms. Copeland also represents Betty Cohen, the owner of a no-dog condominium unit at the Bay Club in Bayside, Queens. Ms. Cohen, who says she suffers from depression, acquired two West Highland terriers and requested a disability accommodation for them. After she submitted letters from her doctors attesting to her condition, the Bay Club said yes to one dog, but notified her that she had to remove the second from the premises by Sept. 30.

“I can’t live without both dogs,” Ms. Cohen said. “No matter what it costs or what I have to do, I have to have them.”

Barbara Morley, the president of the Bay Club’s board of managers, explained the building’s decision in an e-mail, noting that the documentation Ms. Cohen submitted, which was reviewed by legal counsel, “did not support a need for two dogs.”

“Over the last decade we have extended ourselves to accommodate people with special needs who request permission to keep an emotional-support dog,” Ms. Morley wrote, adding that the increase in “comfort dogs” in the building had increased the number of complaints from other residents about dogs barking and soiling carpets. “Many have purchased apartments here because of the no-dog policy,” she said, “and so it is the responsibility of the Board of Managers to consider the concerns and needs of all residents.”

As of last week, Ms. Cohen had not decided what she was going to do, but Ms. Copeland said one option would be to submit a discrimination complaint to the federal Department of Housing and Urban Development Office of Fair Housing and Equal Opportunity.