NEW HAVEN — A police detective, who acknowledged in a sexual harassment complaint that she was paid overtime for shifts she didn’t work, has applied for a disability pension.

Detective Julie Raymond, 38, an 11-year veteran, filed paperwork this week for a pension that would pay her $37,292 annually if it were approved, according to the city. She’s claiming a work-related injury suffered when her knee was struck by a battering ram during a raid.

While her application likely will garner more interest than most because of her well-publicized allegations and admissions, Jerry Sagnella, the city payroll administrator, said the city is “treating it as a normal administrative process.”

Raymond will be sent for an independent medical examination by the city and if it is determined that her knee injury has rendered her unable to perform the duties of a police officer, then the file will go to the police and fire pension board for action.

Last July, Raymond filed a complaint with the state Commission on Human Rights and Opportunities alleging her former boss, Lt. William “Billy” White, sexually harassed her, and that the city did nothing to stop it.

Included in the complaint were statements that, starting in November 2006, White insisted that she take overtime for shifts she didn’t work, despite her repeated protestations.

White, 64, is facing federal prison time in an unrelated FBI corruption probe.

But her pension request adds a unique dimension: Are Raymond’s pension calculations artificially inflated by pay for overtime she never worked?

According to Sagnella, her potential pension would be calculated based on her earnings during fiscal 2006-07, which would be the same timeframe when she said she received fraudulent overtime. It’s unclear precisely how much overtime she worked in that span, but city records show it is less than $15,000.

Fire Department Lt. James Kottage, who serves as chairman of the pension fund, said Raymond, under the union contract, is entitled to the disability pension if medical documentation supports it.

But he added that he also has an obligation to the integrity of fund.

“As the fiduciary to the pension fund and with her admissions to putting in fraudulent overtime slips, I have an issue with that. That needs to be investigated, and the proper numbers need to be used,” Kottage said.

After her overtime admissions became public and New Haven State’s Attorney Michael Dearington informed the city that he wouldn’t consider any investigations she participated in, Police Chief Francisco Ortiz Jr. placed her on modified restricted duty.

Raymond has not been charged with any wrongdoing.

In her CHRO complaint, Raymond said White told her she should not tell anyone about the overtime and she didn’t, because “his comments scared me because I do know how much power Lieutenant White has, not only in the Police Department, but in the city of New Haven as well.”

Her attorney, Jake Donovan of Cromwell, said there is important context that should be known. When White started putting in overtime slips for her, he said, Raymond worked shifts she wasn’t paid for in an effort to offset funds she improperly received.

“I think a careful analysis of the records is going to show that that’s the case,” he said. “It’s her position that she was not compensated for hours that she didn’t work.”

There is an ongoing investigation into the matter, he added, although he declined to elaborate.

That investigation isn’t being conducted by New Haven police. So far, no internal probe has been launched because the FBI still has not returned records it seized in the White case that investigators here would need, said Ortiz.

“All we had was the letter from Mr. Dearington’s office. I have not been able to move internally on anything at all. We are literally at the mercy of the feds.”

In the complaint, Raymond says that after she was promoted to detective in 2005 and was assigned to the narcotics squad, White began trying to establish a romantic relationship and became increasingly aggressive in the efforts, even after she repeatedly said she wasn’t interested.

Sometime after November 2006, White began submitting bogus overtime slips for her against her will, Raymond said.

White was arrested in March 2007 after an eight-month FBI investigation into corruption in the narcotics squad. Three police officers, three bail bondsmen and two Superior Court workers have been arrested, and all but one entered guilty pleas.

Police board Chairman Richard Epstein, who also sits on the pension board, declined to comment on Raymond specifically, but said in general the need for pension language changes is no secret.

Currently, there is no “bad boy” clause that could change a pension of an officer accused of abusing the public trust. White is receiving an annual pension of more than $90,000. A second detective who pleaded guilty is receiving a $41,000 annual pension. Another detective facing charges he stole from the confidential informants fund is getting $58,000 a year.

“The pension board has discussed it. The Board of Police Commissioners has discussed it. The mayor has discussed it. The Board of Aldermen has discussed it,” said Epstein. “It’s not a good system, and I hope it is addressed in the next police contract.”