Lawyers for the family also said that M.I.T.’s student support services were inadequate and that while some campuses — notably, the University of Illinois — had long ago put in place programs that reduced the rate of suicides, the rate at M.I.T. remained disturbingly high.

M.I.T. argued that Mr. Nguyen had been dealing with mental health issues long before he came to M.I.T., including two previous suicide attempts, and that while at M.I.T. he received care from nine different mental health professionals — none of whom had any affiliation with the university and none of whom deemed him at “imminent risk” of killing himself.

Moreover, the university said, Mr. Nguyen “repeatedly declined to avail himself of support resources M.I.T. offered.” Mr. Nguyen had written in an email to the university that he wanted to keep his mental problems separate from his academic issues.

M.I.T. said that if the court sided with the family, it would “transform the relationship between faculty and their students.”

In a brief supporting M.I.T., 18 other Massachusetts universities, including Harvard University, Amherst College, Smith College and Boston University, warned that requiring nonclinical faculty to prevent potential suicides could have disastrous effects. Professors, in seeking to protect themselves from liability, they said, might go overboard in monitoring students, which could drive students underground and dissuade them from talking to anyone about their problems.

In its ruling Monday, the high court affirmed a lower court’s decision and ordered the case be dismissed. It noted that the university could do little when Mr. Nguyen repeatedly refused offers of help. “In these circumstances, as a matter of law, a twenty-five-year-old graduate student’s rights to privacy, autonomy, and self-determination were properly respected,” the court wrote.

The court also exonerated the professor who warned that M.I.T. could have “blood on its hands.” The judges said the remark was “stated metaphorically” and in a different context, not based on explicit statements by Mr. Nguyen that he intended to take his life.