The petition illustrated some of the difficulties of regulating nonprofit organizations, a responsibility that falls to the attorney general’s charities bureau. New York State does not have a law making charities fraud a crime, and criminal prosecutions usually involve larceny, embezzlement or tax fraud.

The foundation’s telephone number has been disconnected, and calls to Mr. Shor’s personal line went unanswered on Monday. Mr. Shor’s lawyer, Douglas Gross, said that he had not seen the petition but that Mr. Shor denied any wrongdoing.

“We do not believe that any of the attorney general’s allegations have any substance,” Mr. Gross said. “Mr. Shor began this charity and ran it with the best of intentions.”

Mr. Shor’s title was president of the foundation until 2010, when, the court papers said, he “nominally resigned that position” after it became known that he had been convicted of bank fraud in 1999.

The court papers said Yehuda Gutwein, the foundation’s accountant, became president but Mr. Shor continued to control the decision-making. Mr. Shor remained so much in charge, the court papers said, that Mr. Gutwein did not know who the foundation’s directors were. When lawyers from the charities bureau handed him a list of the directors, he said he had “no idea who these people are.”

Mr. Gutwein, reached for comment on Monday, said his lawyer would be in touch.

The petition said Mr. Shor admitted to investigators that the foundation never had a registry for bone marrow donors. The court papers said the foundation’s activities about bone marrow work “were limited to him encouraging callers to become donors, and referring people to their local blood bank.”

Mr. Shor also claimed the foundation was “banking stem cells” in liquid nitrogen at extremely cold temperatures, the petition said. But he told investigators that the foundation had never collected or stored what is known as cord blood.