The N.C.A.A. sent a letter of inquiry to Michigan State University, formally opening an investigation into how the university handled the case of Lawrence G. Nassar, the doctor who sexually assaulted scores of female athletes.

Dr. Nassar spent decades on the faculty at the university and treated its athletes, as well as members of the United States national gymnastics team.

“The N.C.A.A. has requested information from Michigan State about any potential rules violations,” Donald M. Remy, the association’s chief legal officer, said in a phone interview Tuesday evening.

N.C.A.A. bylaws require colleges to protect the health, safety and well-being of athletes. Among those who have said Dr. Nassar abused them are members of the Michigan State cross country and softball teams. Kathie Klages, the former gymnastics coach who retired last year, has been accused of seeking to cover up allegations against Dr. Nassar, who served as team physician for the university gymnastics and women’s crew programs.