The NYPD detectives who stopped a lunatic who attacked three people at Grand Central Terminal with a machete on Saturday were working overtime as a part of a crime-fighting initiative.

But sources say department-wide OT cuts are eating into extra subway shifts.

The NYPD disputed this. “The NYPD authorizes 5,000 hours of overtime a day in the subway system,” said a spokesperson. “That has been the case for more than a year, since January 2025. It has not been cut by even a single hour since then.”

A longtime cop told The Post department-wide OT “has been getting cut back for the last year and a half. They’re minimum-manning a lot of these subway stations because there’s a certain [overtime] cap that they don’t want you to go over. “If you go over that cap, [NYPD brass] will bury the commanding officer.”

The NYPD began cracking down on overtime under ex-Mayor Eric Adams, seeing a $1.1 billion drop-off last fiscal year compared to fiscal 2024. Cuts have gotten deeper under soft-on-crime Mayor Mamdani, who campaigned on eliminating the NYPD’s OT budget.

New rules that went into effect on Jan. 1 slashed the number of overtime hours cops can work in half, The Post has reported. And detectives are now limited to 40 hours of total OT a month.

As for extra transit details, sources told The Post that detectives are now limited to “no more than two transit details” a month. They used to be able to work four to six OT shifts underground.

The Mayor’s Office did not return messages.