https://www.marketwatch.com/story/theres-been-a-spike-in-university-enrollments-of-emotional-support-animals-2018-06-21
It would be simpler just to designate one of the dorms as the pet dorm and charge students there an additional deposit.
I don't want to over-generalize but I personally know 2 people who went on the internet, bought a "service animal" vest/halter, and threw it on their dog with no training, no certification, nothing. When asked, one person said "Oh, I just don't want to leave Binkie in the car when I go shopping." I have no problem with legitimate service animals but some of these are counterfeits.
I think it's one of those state/local thingies. You could google it. My first question would be "Why would you want to?" You going to bring the cat to the store? Do you really need to or you just think it would be fun? Personally I really like animals but I don't know if I need to go out to a restaurant and have half the people bringing their pets. Seeing-eye dogs are very cool and I'd heard of dogs that can tell if someone is going to have a seizure and that seems like a good thing but what about that goofy story from a few weeks ago about the person who got all bent out of shape because they couldn't bring their "emotional support" peacock on the plane. To me that's just bizarre. I mean I don't even let my dog get on the couch.