“These boards are often populated with private-sector leaders who would never tolerate such bad behavior in the companies they run,” said Darren Walker, the president of the Ford Foundation, who recently stepped off City Ballet’s board. “Because they’re volunteers, they often yield to management and particularly to charismatic artistic leaders. When presented with evidence to the contrary, they sometimes look the other way.”

Some board members occasionally tried to challenge Mr. Martins, including the prominent longtime benefactor Anne Bass, who finally left the school’s board in 2005. In her resignation letter, recently obtained by The New York Times, Ms. Bass expressed dismay that Mr. Martins “and those who report to him are operating with no oversight or appropriate review and are answerable to no one.”

Now, as the boards prepare to replace Mr. Martins, many former dancers — about two dozen of whom have complained in interviews about his treatment — are concerned that board leaders and others at City Ballet are not examining their own responsibility for allowing a powerful leader to go largely unchecked. Jennifer Desaulniers, who spent three years in the school in the late ’90s, said Mr. Martins openly berated ballerinas if they gained weight and discounted them if they got hurt — and no one stepped in to stop him.

“You’re injured, you’re out; you’re fat, next person,” Ms. Desaulniers said, adding that instructors were also coldhearted. “It goes way beyond Peter — they’re protecting one another, and they’re protecting Balanchine’s legacy.”

Asked to respond, City Ballet said in a statement: “When the current board and management received the anonymous letter suggesting inappropriate actions by Peter Martins, they immediately engaged an independent outside counsel to begin an investigation into the allegations. The board and management take these allegations very seriously. Since the investigation began Mr. Martins has announced his retirement but the investigation into the allegations surrounding him is continuing.”