The city Department of Education has awarded contracts worth up to $101 million to the NYC Leadership Academy — but didn’t keep track of where the money went, a bombshell audit by City Comptroller Scott Stringer charges.

The Long Island City-based non-profit has collected $45.6 million from the contracts to coach “aspiring principals” and teachers. But the DOE failed to produce records to prove the $183-an-hour coaches did what they were paid for.

“If the DOE can’t be sure whether or when the professional coaching even happened, how do we know it was effective?” Stringer asks in a scathing report obtained by The Post.

The contracts also require progress reports and meetings to monitor the vendor’s performance, but the auditors found none — raising the specter of “waste, fraud and abuse,” the report says.

“These failings point to a broken procurement system that allows the DOE to spend freely, devoid of oversight,” Stringer concludes. “Our principals deserve better than this.”

The DOE entered into three contracts with the academy since 2008, the first two under then-Mayor Bloomberg. The third, for payments up to $45 million from July 2014 to June 2019, was inked under Mayor de Blasio by Chancellor Carmen Farina’s chief operating officer. About $34.8 million available remains unspent.

Last month, de Blasio declared a “NYC Leadership Academy Day,” and declared the outfit “an important partner” in running city schools. Fariña praised the academy “for its tremendous work to prepare and support great school leaders.”

But the academy, founded in 2003, has also become notorious for graduating inept — and sometimes corrupt — principals with little teaching experience. Its “leadership coaches,” mostly retired principals, have also been hired in the mayor’s three-year-old Renewal program for struggling schools, which has shown meager academic gains.

The comptroller’s auditors reviewed $559,667 in DOE payments to the academy, including $394,007 for “leadership coaching.”

“Disregarding the safeguards in its own contracts and procurement rules,” the comptroller said, the DOE spent $385,612, or 98 percent of the coaching payments, without the required documentation.

No sign-in sheets were produced at the time showing the dates and hours each coach worked. The academy simply billed for a total number of hours, the audit found.

The absence of records made it virtually impossible to find fake bills or bill-padding, said Stringer spokesman Devon Puglia.

But he added: “Based on what we know from this and other audits of the DOE, we can say that the risk of improper payments is very real.”

More alarming, the DOE “did not request or receive any progress reports,” which the contracts require quarterly. Nor did DOE officials meet monthly with academy officials — another layer of oversight the contract requires. The DOE listed phone calls and other “check-ins,” but had no memos or reports on what was discussed.

The academy’s president and CEO Irma Zardoya, a former Bronx superintendent, collected $260,000 in pay and benefits in 2015-16, according to the group’s latest tax filings. She did not return a message.

The DOE said it’s reviewing the audit. “We’ll continue our work to improve and reinforce the procedures we have in place that serve students, schools, and taxpayers,” said spokesman Will Mantell.

But officials said the DOE stopped using most of NYCLA services in June.

Principals who received training at the leadership academy:

Marcella Sills

PS 106, Far Rockaway

Frequently played hooky while students lacked basics such as textbooks, and watched movies instead of getting gym and art. Dubbed “The School of No.”

Fired after findings of “extreme misconduct” and fraud.

Namita Dwarka

William Cullen Bryant HS, Astoria

Teachers charged she sanctioned grade-fixing, credit schemes, Regents exam cheating, and retaliated against whistleblowers.

Remains principal.

Howard Kwait

John Bowne HS, Flushing

City paid $500,000 to settle multiple sex-harassment suits; assistant principal accused him of grade-fixing.

Remains principal.