NYPD officials had sex with a prostitute dressed as a flight attendant during at least one trip on a private plane paid for by a businessman at the heart of a federal probe into police corruption, The Post has learned.

Police brass joined the “Mile High Club” with the woman after departing from New Jersey’s Teterboro Airport en route to Las Vegas in 2014, sources said.

The call girl repeated her “Coffee, tea or me?” routine when the cops flew back from Vegas, sources said.

“It was first-class plus, with full service,” said a source close to the case.

“They weren’t on commercial airlines. The entertainment was quite good on board.”

Jona Rechnitz, who is under investigation in a suspected gifts-for-favors scheme, provided the high-priced transportation, the sources said.

It was unclear who paid for the prostitute’s services and how many trips took place.

But both Rechnitz and Jeremy Reichberg, another subject of the joint FBI-NYPD probe, accompanied the cops during one getaway to Sin City, a source said.

Deputy Inspector James Grant and Detective Michael Milici were both identified by the sources as having been on board during at least one wild cross-country trip.

Grant, formerly commanding officer of the Upper East Side’s 19th Precinct, was stripped of his badge and transferred earlier this month, hours after The Post revealed that he was suspected of accepting cash and diamonds from Reichberg.

He was sent to the NYPD’s Medical Division in Queens.

Milici, a longtime community affairs officer in Borough Park, Brooklyn, was also placed on modified duty after invoking the Fifth Amendment in front of a federal grand jury, sources have said.

He has been assigned to the Courthouse Division.

Lawyers for Grant and Milici each said they “deny the allegations” about their married clients. Rechnitz declined to comment.

Reichberg’s lawyer said, “Jeremy Reichberg is a good man who has helped many in his community. He has not committed any crime and does not deserve the constant false attacks to which he has been subjected in the press.”

Last week, Police Commissioner Bill Bratton told The Post that the unfolding corruption scandal was the worst he had seen since the rampant, top-to-bottom bribery exposed by the Knapp Commission in the early 1970s.

In addition to the allegations involving top NYPD officials, sources have said that the feds are investigating Mayor Bill de Blasio’s campaign finances and the actions of his former fundraiser Ross Offinger.

Rechnitz was a top “bundler” of campaign contributions to de Blasio, and Reichberg hosted a fundraiser for Hizzoner’s Campaign for One New York.

With Bruce Golding