Mr. Tankleff and his lawyers contend that the killers were Mr. Steuerman and a band of three ex-convicts led by Joseph Creedon, who has admitted collecting debts for drug dealers. These men have publicly denied involvement, but, according to witnesses in Mr. Tankleff’s appeal, have made private admissions.

Before the murders, Mr. Steuerman had been resisting Seymour Tankleff’s demands to repay a $500,000 debt, and they fought over control of the bagel shops they operated together. He was at the Tankleff house for a poker game the night of the attacks, in September 1988.

The book quotes a startling statement by Mr. McCready, the police investigator, in an outtake of a 2006 segment on a “Dr. Phil” television program on the case. Responding to allegations that he was paid $100,000 to shield the killers from investigators, Mr. McCready disputed the sum, by saying of Mr. Creedon, “I mean I think he only got paid $50,000 to do the murder.” The book says that Mr. McCready’s comment, in a taped speakerphone interview that was cut from the broadcast, not only accepted that Mr. Creedon was involved in the killings and was paid for it, but also gave a figure that had not previously been reported.

Mr. Creedon’s lawyer, Anthony M. La Pinta, dismissed Mr. McCready’s statements about the payment for the murders. “This is a ridiculous allegation,” he said.

Richard Firstman, a former reporter for Newsday who wrote the book along with Jay Salpeter, a private investigator, said he discovered another revealing “Dr. Phil” outtake after the book went to press. In that clip, Mr. McCready appears to be discussing Mr. Steuerman’s motive: “Nobody ever talks about the real thing behind the murder itself and the argument with Seymour, between Seymour and Jerry. The argument was over two businessmen, and one outfoxed the other, and one got mad and wanted his money back.”

Combined with his comments about Mr. Creedon, Mr. McCready in the interview effectively embraced Mr. Tankleff’s version of what and who were behind the killings  not the prosecution’s theory and his own testimony that Mr. Tankleff was a spoiled teenager who killed his parents to inherit their wealth.

New accusations about Mr. McCready’s own involvement with Mr. Steuerman were raised by two new witnesses cited in the book. One witness, who gave a statement to Mr. Tankleff’s lawyers but said she was afraid to testify, said that she worked at one of the bagel stores with Mr. Steuerman’s son, Todd, a convicted drug dealer. She said he sold drugs at the store and told her that the police took payments to ignore the illicit activity.