A female NYPD cop was slashed in the face in Brooklyn Sunday morning by a madman armed with a 14-inch butcher knife after he entered a police precinct by the back door, authorities said.

Officers chased the attacker and shot him dead after he refused to drop the knife and lunged at a cop, NYPD Chief of Patrol Philip Rivera said.

The attack happened after the man tried to enter the 73rd Precinct in Brownsville via an employee entrance about 5:28 a.m. When a cop stopped him and told him to go through the front door, he pulled out a knife and slashed her in the face, Rivera said.

A knife-wielding madman tried to enter the 73rd Precinct in Brownsville before slashing an officer. Luiz C. Ribeiro for New York Post

NYPD Chief of Patrol Philip P. Rivera speaks during a press conference as a detective holds a photograph of the butcher knife used to slash a female officer inside the station house. Luiz C. Ribeiro for New York Post

The attacker was then chased down the street by officers. Diego Luzuriaga/FreedomNewsTV

Law enforcement sources told The Post that the knifeman appeared to be trying to cut open the cop’s throat with his surprise attack.

The heroic female officer — who is the daughter of two NYPD detectives, whom of whom is still on the force — was able to block her attacker’s blade with her arm but was cut on the top of her head and her left ear, PBA President Patrick Hendry told The Post.

Another officer then Tasered the man, who fled out the back entrance of the precinct with cops in pursuit.

The attacker, a man in his 40s, then brandished a knife and charged at cops outside a housing project on Saratoga Avenue about two blocks away, Rivera said.

He was shot several times by multiple officers and rushed to Brookdale Hospital in Brooklyn, where he died on arrival.

Location map of the incident. Falon / NY Post Design

The attacker entered the precinct using the back door. Luiz C. Ribeiro for New York Post

The attacker was declared dead upon arrival at the hospital. Luiz C. Ribeiro for New York Post

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Hendry praised the officer’s brave actions and said her parents had been to see her in the hospital.

“Being a police officer is in her blood. But her parents see their daughter in a hospital, it’s very traumatic for them,” he told The Post.

“But she did a tremendous job here tonight,” he added. “She could have been killed here. This knife was coming right for her, but she was able to block off. She used incredible skill, and thank God she was able to do that, and she was able to save many lives out here on the street because we don’t know what he was capable of doing.”

Hendry added that the officer’s actions were a credit to the NYPD.

“She knew that her goal was to get this individual off the streets, he said. “She knew that he was a danger to the people in this neighborhood, and she didn’t care that she was injured at that point. She wanted to stop the threat, and that’s what she did. She made chase along with other police officers.”

The officer’s head wound is described as minor by the police. She is “in good spirits,” Rivera said.

“This situation could have turned out very differently,” he said. “This is the risk that every NYPD officer faces every single day.”