You can decide whether you will rent your apartment to a person with an animal. But by law, these animals are a kind of therapy for their illness. An emotionally supportive animal is not a pet. It is usually not limited to species. In some states, you have no right to refuse to rent to such a client. But there are probably different nuances, so you should check here
https://www.esaregistration.org/emotional-support-animal-guide/ . Tell me, why are you asking this question? Did his dog do something to your house?