New York(CNN)A 20-year-old woman pushing a baby in a stroller was shot in the head at close range and killed Wednesday night on Manhattan's Upper East Side, police said -- a brazen crime that comes amid a push to curb gun violence in New York City and heightened attention to its scourge nationwide.

Authorities believe the victim and the shooter knew each other, calling it a domestic incident, and they've identified a person of interest they want to speak with, a senior law enforcement official said. The 3-month-old baby was not harmed, police said.

The woman is believed to be the child's mother, several law enforcement officials told CNN. Authorities determined she was temporarily living in a building several blocks away, which is a women's shelter, one of the officials said.

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The assailant approached the woman as she pushed the stroller and shot her once in the head around 8:20 p.m. near the intersection of East 95th Street and Lexington Avenue, police said. The shooter, described as a male wearing a black hooded sweatshirt and black sweatpants, left on foot along 95th Street, police said.