The NYPDis sending detectives to bolster the city’s Department of Investigation, The Post has learned. 

As the watchdog agency conducts its own inquiry into an alleged sex-for-overtime scandal at police headquarters, newly appointed Police Commissioner Jessica Tisch on Thursday moved eight detectives and a lieutenant from NYPD investigative squads to DOI.

DOI probes corruption, fraud and other crimes inside city agencies.

The move comes as Tisch attempts to get ahead of the burgeoning scandal involving disgraced ex-Chief of Department Jeffrey Maddrey, which has also prompted probes by the feds and the Manhattan district attorney.

DOI spokeswoman Diane Struzzi said the transferred personnel won’t be directly investigating the sex-for-overtime allegations, which will be done by former prosecutors and other non-NYPD employees.

“These transfers ensure a fully-staffed DOI detective squad, which has historically been a part of DOI and assists DOI with its investigations,” Struzzi said.

Tisch is also looking to bring the NYPD’s overtime under control and has issued a Uniformed Overtime Management Plan “to stem abuse” that includes overtime limits, according to a memo obtained by The Post.

“These thresholds are by no means an entitlement,” the two-page missive states.

Each boss will be responsible for appointing compliance officers to monitor and track overtime and produce monthly reports to be sent to the budget office, the memo shows.

“This monthly report will detail, by individual, overtime variance, if any, and the reason for it,” the memo states.