Officers opened fire when a woman reportedly lunged at them with two knives Sunday night. The incident happened in front of a women's shelter on East 45th Street near Second Avenue.
It ended with two officers firing multiple shots to bring down the woman they say was advancing on them with an ornate knife in each hand.
"It was like four loud, loud bangs. I can't describe it. I've never heard gunshots before," one witness said.
Police say the woman had ignored repeated orders to drop her knives. They say she had one hand raised in a plunging position when the officers opened fire.
The woman was rushed to Bellevue Hospital, where she was pronounced dead on arrival.
Investigators say the woman had been fighting outside with another resident of the New Providence Women's Shelter, which is a substance abuse shelter, a former convent and orphanage, housing about 130 women.