Nassau prosecutors failed to fulfill an ethical obligation by not turning over an anonymous letter to lawyers for ex-public health system executive Larry Slatky before his corruption trial began, a judge ruled Wednesday.

But Nassau Supervising Judge Christopher Quinn also said there was no clear finding that the district attorney's office violated a legal principle known as the Brady rule. That rule says prosecutors have to disclose evidence favorable to a defendant's case.

Slatky, 65, of Cold Spring Harbor, is on trial in Mineola after pleading not guilty to two misdemeanor official misconduct charges after an indictment last year.

Authorities say Slatky abused his power while chief operating officer of NuHealth -- a public benefit corporation that includes Nassau University Medical Center -- when he directed subordinates to award a laundry contract to a friend's company in 2010.

In his decision, the judge said the anonymous dispatch alleged corruption against people who included three of the prosecution's witnesses against Slatky. He wrote that the letter spoke of "the awards of these very services" that are subject of the accusations against the defendant.

Reacting to the decision, Shams Tarek, a spokesman for acting District Attorney Madeline Singas, said in a statement: "While the judge agreed that there was no Brady violation here, we maintain that prosecutors acted ethically and out an abundance of caution in turning over an anonymous letter containing broad and unsupported allegations."

Brian Griffin, an attorney for Slatky, had asked Quinn to dismiss the charges after the document's disclosure during the trial. However, prosecutors argued the letter was "just rumor" and wasn't Brady material.

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The judge didn't dismiss the charges but criticized the district attorney's office, saying the prosecution had the letter for 22 months before turning it over. "The court is troubled by not only the contents of the letter, but also the length of time . . . in the people's possession, the fact that it was never investigated, and the fact it was not disclosed to the defendant," Quinn's decision said.

His ruling added: "Due process of law requires that the defendant be given a full and fair opportunity to defend himself. The court believes that his right has been hampered."

As a result, Quinn said he would draw an "adverse inference" regarding certain testimony. That means as he decides the nonjury case, he may consider the allegations in the letter when evaluating the credibility of witnesses it named.

"All Mr. Slatky has wanted from the beginning is a fair trial where the truth would come out. Any efforts to thwart that are very troubling," Griffin said Wednesday.

The trial continues Thursday.