Rachel Brill and Mary McCarthy are seniors and longtime roommates at St. Mary’s College of Maryland. This year, they share their four-bedroom campus apartment with two other female students. Also, Theo and Carl.

Theo, easygoing and unflappable, is a tawny, 103-pound, longhaired German shepherd. Carl, an energetic charm magnet, is a jet-black, 1.5-pound Netherland Dwarf rabbit.

House rules: Carl must reside in a pen under McCarthy’s raised bed; Theo snoozes in a crate in Brill’s bedroom. Carl cannot be let loose in the living room, where Theo likes to hang out. “We’re still very careful because we don’t want there to be an issue with Theo and Carl,” McCarthy said. “We’re both very anxious people.”

And that is exactly why Theo and Carl have permission to live in campus housing.

Like many schools across the country, St. Mary’s, a small, public liberal arts college, is figuring out how to field increasing requests for animals by students with diagnosed mental health problems. Last fall it began allowing “comfort animals” for students such as Brill, Theo’s owner, who has anxiety and depression, and McCarthy, Carl’s owner, who gets panic attacks.

Anxiety, followed closely by depression, has become a growing diagnosis among college students in the last few years. The calming effect of some domesticated animals has become so widely accepted that many schools bring in trained therapy dogs to play with stressed students during exam periods.

But as students with psychiatric diagnoses are asking to reside on campus with their own animals, schools with no-pet housing policies are scrambling to address a surfeit of new problems. How can administrators discern a troubled adolescent’s legitimate request from that of a homesick student who would really, really like a kitten? If a student with a psychological disability has the right to live with an animal, how should schools protect other students whose allergies or phobias may be triggered by that animal?

The topic is being hotly debated by college housing and disability officials in the wake of discrimination lawsuits filed by students who were denied emotional support animals. Last month, on the eve of a trial in a case closely watched by administrators, the University of Nebraska at Kearney settled with the Justice Department, agreeing to pay $140,000 to two students who had been denied support animals, and spelling out protocols for future requests. Recently, a federal judge refused to dismiss a similar case against Kent State University.

“The disabilities services people are all looking at what they need to do to make this work,” said Jane Jarrow, an educational disabilities consultant who is teaching “Who Let the Dogs In?” — an online course about emotional support animals — for the fourth time this year. “We’re way past pretending it’s not going to happen.”

In the years before support animal lawsuits, universities found it relatively easy to say no to requests for animals. But now, said Michael R. Masinter, an expert on disability law at Nova Southeastern University in Florida, “schools think it’s easier to say yes than no because property damage is cheaper than litigation.”

The overwhelming majority of support animal requests are for dogs and cats. But schools have had requests for lizards, tarantulas, potbellied pigs, ferrets, rats, guinea pigs and sugar gliders — nocturnal, flying, 6-ounce Australian marsupials.

Clearly, many requested animals are students’ pets. But what is the difference between an emotional support animal and a pet that also provides support?

The distinction depends less on the animal and more on the student: whether the student has a diagnosed psychiatric disorder, and can document that the animal is therapeutically necessary.

“Do we have people trying to get their pet across as an assistance animal? Sure,” said Jamie Axelrod, director of disability resources at Northern Arizona University, where requests for support animals rose to about 75 last year from a handful a few years ago. “Do we have people who legitimately require one? We do.”

“You have to rely on a treatment provider’s ethical sense that they’re doing what’s right for their patient,” Axelrod added. “But it’s a new gray area.”

Research on the therapeutic value of animals is limited. Some studies have shown they can provide a short-term benefit, particularly in reducing anxiety and depression. A long-term therapeutic benefit, however, has not been definitively established by randomized control trials.

Joanne Goldwater, associate dean of students and director of residence life at St. Mary’s College of Maryland, is not concerned about objective evidence.

“Having that animal has clearly helped to reduce stress and anxiety for some students,” she said, “which helps them progress towards their degree.”

Whether schools must permit support animals depends, generally, on federal housing law. The Nebraska suit was filed by the Justice Department in 2011 on behalf of Brittany Hamilton, whose 4-pound miniature pinscher, Butch, would put his paws on her shoulders to quell her anxiety attacks. She wanted Butch to live in her university apartment. The university said no.

But in 2013, a federal judge ruled that the university’s residences were bound by the Fair Housing Act, which protects individuals with disabilities from discrimination. Among the act’s “reasonable accommodations” for residents with psychological disabilities are animals that provide emotional support.

Although the consent order in the Nebraska case last month is not binding on other colleges, it lays out some guidelines. The university can deny a request if the animal is too big for the quarters or aggressive, or damages property.

And if a student’s documentation looks insufficient, a school can contact the student’s medical provider — a pushback against emotional support animal letters downloaded on the Internet or churned out by cybertherapists who, for fees of up to $150, will Skype with the student and then issue the document. Universities have been circulating a watch list of such practitioners.

Some institutions are managing the issue with a matter-of-fact attitude.

“We use our code of conduct for animals as well as people,” said L. Scott Lissner, the Americans With Disabilities Act coordinator at Ohio State University. “We don’t let our students walk across campus and lick people unless it’s welcome, so we don’t let the dogs do it. We don’t let students howl all night.” And, he added, “They can’t go to the bathroom wherever they want.”