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Gunshots were fired early on Tuesday in the parking lot of the Resorts World Casino in Queens. The police were called, and officers discovered a 55-year-old woman slumped in her car, fatally wounded.

A suspect, a former boyfriend, then sent taunting messages to the woman’s friend and called the woman’s family. He was quickly tracked to East New York, Brooklyn, where three plainclothes officers shot and killed him in a hail of more than 20 bullets after he opened fire on them, the police said.

The police identified the gunman as Dalton Branch, 51, an ex-convict with a long history of arrests who lived in Brooklyn.

Mr. Branch was involved in “a prior relationship” with the woman he shot, Patricia Mohammed, said Robert K. Boyce, the chief of detectives for the New York Police Department.

In the minutes after the shooting, Mr. Branch sent a series of harassing text messages to a man who was with Ms. Mohammed just before the shooting, but who was not injured, Chief Boyce said. In those messages Mr. Branch referred to himself as “the grim reaper,” the chief said. He also called relatives of Ms. Mohammed, “taunting them as well,” he said.

Photo Dalton Branch Credit NYPD, via Associated Press

Chief Boyce provided details as he stood near the location of the Brooklyn shooting, on Pennsylvania Avenue, near a rented white Dodge Charger he said Mr. Branch had been driving.

Retracing the events of the morning, the chief said 911 callers alerted the police to the shooting at the casino, near the Aqueduct racetrack, around 2:20 a.m.

There, in the casino’s parking lot, Mr. Branch pulled up to Ms. Mohammed and the 51-year-old man, who were standing outside her black Chrysler, speaking.

From his car, Mr. Branch fired “a round at them,” said Chief Boyce. The man ran and Ms. Mohammed climbed into her car. Mr. Branch got out and fired three times at Ms. Mohammed from the driver’s side, and again from the other side of the car, the chief said. He fired another shot at the man but missed, the police said.

Ms. Mohammed was taken to Jamaica Hospital Center, where she was pronounced dead.

Around 5:40 a.m., a sergeant, detective and police officer from the Queens Warrant Squad saw the Dodge parked in front of 875 Pennsylvania Avenue, near Stanley Avenue, about four miles from the casino, and approached, the police said.

Photo A vehicle involved in the shooting in East New York, Brooklyn. The police said Dalton Branch opened fire on three plainclothes officers who approached him. Credit Kevin Hagen for The New York Times

The man inside, Mr. Branch, pulled out a gun, the police said. He fired from inside his car and then got out “and continued firing on the officers,” Chief Boyce said.

All three officers returned fire from about eight feet away, striking Mr. Branch several times. Detectives recovered videotape from a nearby hotel showing a portion of the encounter but not the shooting, Chief Boyce said.

Mr. Branch was taken to Brookdale University Hospital and Medical Center, where he was pronounced dead, the police said. He had 15 gunshot wounds, though some could be entrance and exit wounds, the police said.

When Mr. Branch was a teenager in the early 1980s, he was shot and wounded by an officer who confronted him in the course of a gunpoint robbery in Queens, according to state records. Convicted in 1983 of first-degree robbery and several counts of weapons possession, he served more than two years in prison.

In 2002, Mr. Branch was arrested again for possession of a gun and loose ammunition when officers with the Brooklyn North Gang Unit executed a search warrant on his home; he was later convicted of weapons possession. In 2005, he told a parole board that the police got information from “an ex-friend of mine” and that he had the weapon for protection.

He said when he got out of prison, his goals would be to find a job and take care of his son and girlfriend, “because she took care of me very much while I was here through all my trials and tribulations.”

Photo Patricia Mohammed

Investigators believe that the woman was Ms. Mohammed.

A woman who answered the phone at Ms. Mohammed’s home on Tuesday afternoon said, “We’re not giving out any information,” and hung up.

Mr. Branch was released in 2006.

Chief Boyce said that Mr. Branch knew the man he shot at; he works as a manager at Trans Express, the bus company hired by the casino to provide free shuttle service, where the police said Mr. Branch once worked. The police said Ms. Mohammed had also worked at the company as a driver, though a spokesman for the casino disputed that.

Near the Dodge, the police recovered a Beretta .380-caliber semiautomatic handgun “in the cocked position,” several shell casings on the ground, an extra magazine clip and an empty box of ammunition, Chief Boyce said.

Detectives also recovered a cellphone they believe belonged to Mr. Branch, the chief said.

“We’re trying to figure this out,” the chief said. “We have not completed our investigation yet.”