A 21-year-old Hofstra University student who was killed in a home invasion on Friday was mistakenly shot in the head by an officer who fired eight times at a man who was holding a gun to the student’s head and then pointed it at him, the police said on Saturday. Seven of the bullets hit the man, who was also killed.

The student, Andrea Rebello, and her twin sister, Jessica, who also lived at the home, just blocks from the university, were among several people taken hostage on Friday morning in an apparent robbery attempt.

The Nassau County police identified the gunman as Dalton Smith, 30, a Hempstead, N.Y., resident with an extensive criminal record who was wanted for violating parole on a robbery conviction.

About 15 or 20 minutes elapsed from the time Mr. Smith burst into the home about 2:20 a.m. Friday until the last shot was fired, the police said.

Several hostages had already escaped when police officers arrived and surrounded the house at about 2:30 a.m., Detective Lt. John Azzata said at a news conference on Saturday. The police, who had been alerted to the invasion by one of the people who had escaped, initially thought that only Mr. Smith remained in the house, he said.

At least one officer had entered the home as Mr. Smith, clutching Ms. Rebello in a headlock with a gun to her head, tried to get to the back door, Detective Azzata said. After noticing the officer in the hallway, Mr. Smith brought Ms. Rebello closer to his body, Detective Azzata said. Mr. Smith then pointed his gun at the officer.

“At that point, the police officer fires several rounds,” Detective Azzata said. “Seven of those rounds struck our subject; one of those rounds struck the victim.”

Ms. Rebello was taken to the hospital, where she died. Mr. Smith’s weapon, a 9-millimeter handgun, had one bullet in the chamber and another in the magazine, Detective Azzata said. He never fired a shot.

Detective Azzata said the officer who fired the shots was a 12-year veteran of the force, but would not identify him or say whether the officer had acted according to protocol. He said the authorities were still investigating the circumstances surrounding the shooting.

At the news conference, Thomas V. Dale, the Nassau County police commissioner, said he had gone to Ms. Rebello’s parents’ home in Tarrytown, N.Y., to personally inform them that it had been a police officer’s bullet that killed their daughter.

Telephone calls made to Ms. Rebello’s parents on Saturday night went unanswered.

Given Mr. Smith’s criminal past, questions are likely to be raised about how he was being monitored.

The authorities issued a warrant for his arrest on April 25, after he failed to check in with a parole officer. He had served multiple sentences in prison, mostly for robbery convictions, and was released on parole in February after serving a nine-year sentence.

It is unclear why Mr. Smith chose the house on California Avenue where Ms. Rebello lived to break into, the police said. At the time of the invasion, Detective Azzata said, the front door of the home had been left open by another resident, who had gone upstairs to get his keys with the intention of moving his car.

While the authorities said Mr. Smith lived in Hempstead, there is no address for anyone by his name in public records.

The invasion left residents near the university fearful at a time when many would be preparing for graduation. Hofstra officials said commencement ceremonies on Sunday would go ahead.

On Saturday, many students were preparing to leave for summer vacation. While many said they felt secure on campus, some expressed concern about security in the neighborhoods surrounding it, where some students prefer to rent houses. Ms. Rebello and her sister lived on a typically quiet block in Uniondale that some said was uncomfortable to walk through after dark.

“Walking after class after 7 p.m. or 9 p.m., it feels really unsafe to walk outside of campus across Hempstead Turnpike,” said Jack Qiu, 20, a sophomore who said he preferred to live in the dorms because they are safer. “If you walk around California Avenue and the streets around them, there are streets there that don’t have street lamps.”

A funeral for Ms. Rebello is set for Wednesday in Tarrytown, N.Y., the Coffee Funeral Home said. She will be buried in Sleepy Hollow Cemetery.

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