A veteran police captain in Los Angeles was subjected to a sexually charged, hostile work environment after a nude photo of a woman was shared among officers, some of whom falsely claimed the image depicted the female supervisor, an explosive lawsuit claims.

The lawsuit, filed by LAPD Capt. Lillian L. Carranza, alleges that department brass knew the “deeply humiliating” naked image was being circulated within the force, along with disparaging comments about her, but didn’t tell the 28-year veteran, the Los Angeles Times reports.

“The chief encourages us to be vocal and transparent, but nothing could be further from the truth when it comes to sexual harassment,” Carranza told the newspaper. “You are given a gag order, and then they do nothing to correct it. Zero tolerance in the LAPD for such behavior is symbolic. The reality is it is tolerated.”

Carranza, 50, was promoted to captain in 2012 and now oversees the LAPD’s commercial crimes division. In her lawsuit, which was filed Friday — one day after she tweeted #MeToo in response to a post about the R. Kelly documentary — Carranza claims LAPD Deputy Chief Debra McCarthy has been aware of the alleged harassment and shared photo since November but “took no steps” to inform her of the purported misconduct.

The photo, according to Carranza’s lawsuit, was shared along with another explicit image of an LAPD detective, Ysabel Villegas, who reported in November that an officer she was having an affair with shared revenge porn of her with other members of the force.

Villegas, who has since received a restraining order against Officer Daniel Reedy, noted in her report to the Glendora Police Department that another woman employed by the LAPD was also the subject of revealing photos being shared throughout the department, the Los Angeles Times reports.

Carranza referred an inquiry on Tuesday to her attorney, Gregory Smith, who did not immediately return a call seeking comment. She previously told the Los Angeles Times that the department has ordered her not to discuss details of her accusations.

“This is indicative of why it is so hard to recruit and promote women here,” she told the newspaper.

Carranza claims in her lawsuit that she explicitly requested that McCarthy and other department officials make clear that the “photograph in question” was, in fact, not her, but nothing was done to relay that or to stop officers from sharing the image.

A police spokesman, meanwhile, declined comment when reached by The Post, citing pending litigation.

Carranza claims she was also victimized in 2013 when a detective supervisor was captured on audio telling her that she was a “very cute little Hispanic lady” who had been “swapped around a bunch of times,” according to her lawsuit. The incidents are part of a sexist culture within the department that subjects women to ongoing verbal harassment, she claims.