A Hofstra University student being held in a headlock at gunpoint by an intruder was accidently shot and killed by a police officer who had responded to the home invasion at an off-campus home, police said Saturday.

Junior public relations major Andrea Rebello was shot once in the head early Friday morning by an officer who opened fire after the masked intruder pointed a gun at the officer while holding the 21-year-old student, Nassau County homicide squad Lt. John Azzatasaid.

In a tense confrontation with the officer, gunman Dalton Smith”menaces our police officer, points his gun at the police officer,”Azzata said. The officer opened fire, killing Smith and his hostage.

Azzata said the Nassau County police officer fired eight shots at Smith, who police described as having an “extensive” criminal background. Smith was hit seven times and died. Rebello was shot once in the head.

“He kept saying, ‘I’m going to kill her,’ and then he pointed the gun at the police officer,” Azzata said.

A loaded 9 mm handgun with a serial number scratched off was found at the scene, police said.

Nassau County Police Commissioner Thomas Dale said he had traveled to Rebello’s Tarrytown, N.Y., home to explain to Rebello’s parents what happened.

“I felt obligated as a police commissioner and as a parent to inform them as soon as all the forensic results were completed,” Dale said.

The veteran police officer, who was not identified, has about 12 years of experience on the Nassau County police force and previously spent several years as a New York City police officer, Dale said.

The officer is currently out on sick leave. He will be the focus of an internal police investigation once the criminal investigation is completed, which is standard police procedure in any officer-involved shooting, the commissioner said.

Earlier Saturday, police announced that Smith, 30, had been wanted on a parole violation related to a first-degree robbery conviction and had an arrest history dating back nearly 15 years.

The shooting came just days before the school’s commencement ceremonies, which are scheduled to take place Sunday.

A university spokeswoman said students will be handed white ribbons to wear in memory of Rebello. The shooting, which took place just steps from campus, has cast a pall over the university community as it geared up for commencement on Sunday.

“Today is the last day of finals and this should be a happy day on campus; but it’s not,” Hofstra freshman Scott Aharoni of Great Neck, said Friday as he passed through the area rife with yellow crime-scene tape. “It’s really sad.”

Rebello was in the two-story home with her twin sister Jessica, a third woman and a man when Smith, wearing a ski mask, walked into the house through an open front door, Azzata said. Smith demanded valuables and was told they were upstairs, Azzata said.

Smith, apparently unsatisfied with the valuables upstairs, asked if any of the four had a bank account and could withdraw money, Azzata said. The intruder then allowed the unidentified woman to leave and collect money from an ATM, telling her she had only eight minutes to come back with cash before he killed one of her friends, Azzata said.

The woman left for the bank and called 911, according to Azzata.

Minutes later, two police officers arrived at the home and found Rebello’s twin sister Jessica running out of the front door and the male guest hiding behind a couch on the first floor, Azzata said.

One of the officers entered the home and encountered Smith holding onto Rebello in a headlock, coming down the stairs, Azzata said. Smith pulled Rebello closer and started moving backward toward a rear door of the house, pointing the gun at her head before eventually threatening the officer, Azzata said.

Rebello’s family declined comment Saturday.

The Rev. Osvaldo Franklin, who gave Rebello and her sister Jessica their first communions, on Saturday night told The Associated Press their mother, Nella, couldn’t even speak to him earlier in the day.

“She was so devastated,” said Franklin. “She’s just crying. We have to pray for Andrea, to pray for Jessica because she needs help.”

Franklin said a funeral is scheduled for Wednesday at Teresa of Avila Church in Sleepy Hollow, N.Y., and will be in Portuguese.

“The family’s a very good family, they have very good values,” he said. “I gave them first communion to Andrea and Jessica and they started to help me in the mass for many years. They are a very good, very devoted family.”