One of the city’s highest-paid surgeons is facing a federal probe for allegedly overbilling patients.

“My Office has an open investigation into the billing practices of Dr. David Samadi,” Jessica Jean Hu, an assistant US attorney in Manhattan, wrote in an e-mail to the Boston Globe.

The doctor, a prostate-cancer specialist who is chairman of urology at Lenox Hill Hospital, had double-booked his surgeries for years, the Globe has reported. The newspaper found that Samadi overlapped operations in about 70 percent of 2,200 surgeries between 2013 and 2016.

Overlapping surgeries where a lower-ranking resident finishes a procedure or performs non-critical parts of the operation is considered acceptable. But Medicare rules forbid teaching hospitals like Lenox Hill from doing concurrent surgeries when the “critical parts” of two operations happen at the same time.

Barbara Osborn, a Lenox Hill spokeswoman, said the hospital was unaware of the federal probe and that Samadi was required “to perform all critical or key portions of any surgical procedure and be immediately available for the entire surgery.”

“Dr. Samadi is a high-quality surgeon with excellent clinical outcomes whose primary concern and priority has always been the well-being of his patients,” Osborn said.

Lenox Hill paid Samadi $6.7 million in 2015, according to the hospital’s latest available tax filing.

Samadi raked in $7.6 million in 2012 when he worked at Mount Sinai Hospital, which made him the highest earner at a New York City hospital that year.

The Lenox Hill Hospital Web site has listed Samadi as an associate professor at the Hofstra/Northwell School of Medicine, something Samadi has claimed in press materials and on his Web site.

But Osborn told The Post his application for an academic appointment was still in the process of being reviewed by the medical school.

When asked about the Web site claim, Osborn said it was incorrect and it was later updated.