For years, Han Duy Nguyen struggled with depression. As an undergraduate at Stanford, he tried to kill himself twice.

When he arrived at the Massachusetts Institute of Technology’s Sloan School of Management, university officials offered him mental health services. His adviser believed he was so vulnerable that he recommended Nguyen should pass his classes regardless of his academic performance.

But on June 2, 2009, after a tense conversation with his adviser, Nguyen, 25, rushed up to the sixth floor of a campus building in Kendall Square and leapt to his death.

Nguyen’s family has filed a wrongful-death suit against MIT, claiming the Cambridge university had a legal duty to protect him from harm.

On Tuesday, Massachusetts’ highest court heard arguments in the closely watched case, which will decide whether colleges can be held responsible for campus suicides.

“Suicide can and should be prevented when possible,’’ Jeffrey S. Beeler, the lawyer for Nguyen’s family, told the Supreme Judicial Court.

The court will decide whether to reverse a Middlesex Superior Court judge’s decision last year that MIT had no legal obligation to prevent the suicide. A reversal would allow a jury to hear the case.

Nguyen’s family also wants the court to rule that the university-student relationship obliges MIT to recognize warning signs of suicide and act on them.

MIT and other colleges say that standard would place an enormous burden on faculty and administrators and could lead them to intervene too aggressively in students’ lives.

“Imposing this rigid, one-size-fits-all duty would require non-clinician employees to take overbroad, potentially intrusive steps to force mental health services . . . on students who do not want or need them,’’ lawyers wrote in an amicus brief supporting MIT’s position. “Students who witness such conduct may be driven underground for fear of overreaction.’’

Eighteen other institutions, including Harvard University and Williams College, signed the brief.

The suicide rate at MIT in recent years has been notably higher than the national average for college campuses, according to a 2015 Globe review of public records, as well as university and media reports. MIT has responded with a range of measures to improve mental health and student support services.

Beeler said Nguyen fell victim to a mental health system plagued by ineffective communication. MIT counselors met with Nguyen in 2007, but they failed to follow up, he said.

Justice Scott L. Kafker asked Beeler what more MIT could have done, given that Nguyen was seeing private psychiatrists and declined offers to see mental health counselors on campus.

“I’m trying to understand their duty,’’ Kafker said. “What are they supposed to do?’’

Beeler said other campuses, like the University of Illinois, have mandated on-campus treatment for students who have threatened suicide.

“It’s why it’s so important that the court adopt this universal common-law standard,’’ he said.

The lawsuit specifically blames two professors, including his adviser, Birger Wernerfelt, the faculty head of the graduate program Nguyen attended. Wernerfelt spoke with Nguyen just minutes before his suicide.

Wernerfelt called Nguyen as he was working in a laboratory to berate him for sending what he deemed to be a disrespectful e-mail to another professor.

“I read him the riot act,’’ Wernerfelt e-mailed the professor at 11:04 a.m., two minutes after Nguyen jumped.

Beeler described the call “an act of malfeasance.’’

“The final phone call with Birger Wernerfelt caused this young man’s death,’’ he said.

Months earlier, Wernerfelt had recommended to his colleagues that they pass Nguyen or “they might end up with ‘blood on their hands,’ ’’ according to court documents.

Justice Frank M. Gaziano asked Kevin Martin, the lawyer for MIT, if that comment did not suggest professors believed Nguyen was a suicide risk.

“The professor who made that statement was a marketing professor,’’ Martin replied. “He was not trained to see when that risk was foreseeable.’’

Gaziano appeared troubled by Martin’s argument that university employees are not legally obligated to stop a suicide. He asked whether that meant a resident adviser is not responsible for stopping a student who is threatening to hang himself in his room.

Martin replied that a school could be responsible if the student had not rejected mental health services in the past.

“A university should not begin treating a student against their will,’’ Martin said. “The problem we have with this case . . . is that Mr. Nguyen’s estate is effectively asking for a duty to be imposed which is contradictory to what Mr. Nguyen wanted when he was alive, which was to be treated like everyone else.’’

Maria Cramer can be reached at mcramer@globe.com. Follow her on Twitter @GlobeMCramer.