The family of a Hofstra University student who died three years ago in an off-campus police shooting during an armed home invasion has filed a federal lawsuit against Nassau County and numerous police officials.

Relatives of Andrea Rebello, who was a 21-year-old junior from Tarrytown, say that police did only a “cursory” probe into the May 2013 shooting by the Nassau County Police Department officer to try to shield the department from liability.

In the civil rights lawsuit, filed Monday with the Eastern District of New York, the plaintiffs also allege Nassau police personnel and supervisors – including 911 operators – weren’t properly trained for hostage situations. In the suit, the plaintiffs -- Rebello’s family and her estate -- allege rights violations including deprivation of life and liberty, infliction of pain and suffering, and loss of a family member and ask for a jury trial and monetary damages.

Both county officials and David Roth, an attorney for the Rebellos, declined to comment Wednesday.

James Carver, president of the department’s largest union, has said previously that the gunman who held Rebello hostage is the only one to blame for her death.

Authorities have said Rebello died after Nassau Police Officer Nikolas Budimlic accidentally shot her in her apartment as armed parolee Dalton Smith, 30, of Hempstead, used her as a human shield. Budimlic also shot and killed Smith in the May 17, 2013, encounter.

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In 2014, a Nassau district attorney’s office review concluded Budimlic wouldn’t face criminal charges and “reasonably perceived threats of deadly force against himself and others and acted accordingly.”

Later in 2014, Rebello’s family initially filed a wrongful death lawsuit against Nassau and its police force in State Supreme Court. That matter remains pending.

The new federal filing claims that even before Rebello’s death, a union for 911 officials was fighting with the county to get state-mandated training that included handling hostage incidents as part of funding to the 911 center.

It also says that a 911 official categorized the incident as a robbery in progress, despite quickly having information from a caller showing hostages were involved, and that the lapse led to a breakdown in the supervision of officers at the scene.

The plaintiffs also say the records police created in the case “were designed to be as sparse as possible,” and alleges police moved around evidence at the Uniondale rental home and destroyed the crime scene as part of “a massive cover-up” to try to guard against civil claims.

The filing also claims the county pressured supervisors into only doing a hasty probe into the officer-involved shooting so the police department’s finding that it was justified – on the same day as the shooting -- wouldn’t be contradicted.

The lawsuit says police never attempted to engage the armed intruder in hostage negotiations, except by yelling at him to drop his weapon. It also claims Budimlic fired the gunshot that killed Rebello “with deliberate indifference” to her life, and that the police department’s manual at that time had no content regarding hostage incidents.