New Orleans — Heather Hilliard, the former chief administrative assistant for public safety in Jefferson Parish, is suing her former employer, alleging that she was sexually harassed by her supervisor and faced retaliatory measures when she complained, including the loss of her job.

The suit, filed Tuesday in U.S. District Court in New Orleans, also alleges that she was discriminated against in her pay, claiming it was significantly less than her male predecessor’s and male successor’s.

Hilliard’s boss, Richard Hart, resigned from his position as deputy chief operating officer for the parish last February. The lawsuit says he quit two days after a report that corroborated Hilliard’s claims was filed by a firm the parish hired to investigate her complaints.

That report was given to Parish President John Young, the suit says, but in public remarks he called Hart’s departure “a tremendous loss to the parish’’ and said he was disappointed to lose Hart’s “vision, energy and expertise.”

Shortly thereafter, Hilliard received an unfavorable job review, and in May, Young fired her, the suit notes.

Hilliard’s suit claims Young’s decision to fire her was “in retaliation for her complaining about John Young’s good friend and political supporter Richard Hart.”

The only response to the lawsuit from the parish was an email from Deborah Foshee, the parish attorney.

“The Parish Attorney’s Office learned this morning of a lawsuit filed last night in Federal Court by former employee Heather Hilliard. This matter is a personnel matter about which we will make no public comment. The litigation will be handled by an outside law firm and we will defer to that law firm for further handling,’’ the email says.

The suit claims that Hart, who was hired in January of 2011, began harassing Hilliard the next month, using sexually offensive language and vulgar comments. The harassment continued and even increased after she asked him to stop, the suit says.

Hilliard complained in person and in writing to Hart’s supervisor, Chris Cox, and when that was not successful, she brought her complaints to Peggy Barton, director of human resources for the parish, and to Foshee, the suit says. It details written complaints beginning in March of 2011 and continuing through December of that year without resolution.

In November 2011, however, Barton decided that the Parish Risk Management Department should investigate Hilliard’s complaints, and the department hired DMM & Associates LLC to conduct the probe, the suit says.

Shortly thereafter, Cox informed the company that the investigation would be handled internally, the suit says, but Foshee contacted DMM four days later to re-engage their services.

The suit says that most of the 21 witnesses interviewed by DMM backed up Hilliard’s complaints.

“The witnesses characterized Hart’s characteristic behavior as demeaning and rude, often diminishing the authority of female managers and supervisors by directing questions to their male subordinates,’’ the suit said.

They also told investigators that Hart made inappropriate hand gestures and that they were afraid of him because he carried a gun at work, the suit claims.

The suit says that the parish failed to promptly investigate Hilliard’s complaints and, that when it did do so, failed to protect Hilliard “against retaliation perpetrated by John Young for whom it is legally responsible.’’