Authorities found the three people dead inside the home on East 56th Street in the East Flatbush section of Brooklyn just before 9 a.m.
The woman's older son, a 19 year old from a previous marriage, jumped out the back window and literally ran into responding police.
The 43-year-old officer was found dead in the first floor apartment with the infant in her arms. The baby was 7 months old.
The bodies were discovered after her son, who was sleeping in his bedroom, awoke to the sound of an argument and saw his mother with a gun, said chief police spokesman Paul Browne.
The young man went back into his bedroom where he escaped through the window and called 911, but by the time police arrived moments later, the three others were dead, Browne said.
The body of the 33-year-old father, Dason Peters, was found in the entry of the first-floor apartment on a quiet, tree-lined street, authorities said.
The bodies of the officer, 13-year veteran of the force Rosetta Samuel, and her baby boy, Dylan, were found face up on the bed in her bedroom. The gun was by her side.
The officer used her service weapon, a semiautomatic Glock handgun. She and the baby were apparently struck in the chest. Peters was shot in the torso. Police say possibly four rounds were fired but it's not clear how many times Dylan and Peters were hit.
The two were a couple but were not married, police said.
The teenager, Dondre Samuel, who is the officer's son from a previous relationship, was uninjured.
It was unclear what prompted the dispute. Police have not discovered a note, and there was nothing in Rosette Samuel's police records to indicate she had been troubled, authorities said. There were no reports of domestic violence.
Ionie Brown-Johnson, a retired health care worker who lives four doors down from Samuel, said the two women would greet each other when the officer took the baby for walks, either cradling him or pushing him in a stroller.
"She looked happy when she walked with the child in her arms," said Brown-Johnson, 73. "I'm asking myself, what could be the cause of her doing this?"
Police were still investigating and had blocked off the street as onlookers in the working-class neighborhood clustered nearby.
Samuel joined the New York Police Department in 2000 and was most recently assigned to a precinct in Queens.
A next-door neighbor who identified herself as an aunt said she could find no reason for the deaths. Agnes Samuel, 83, said the officer was always smiling and waving to her, and seemed like a happy person.
"It's terrible," Agnes Samuel said as she choked up. "For people to take a life like that. Oh, Lord!"
Around the corner from the crime scene, 19-year-old Stephen Elias, a friend of Dondre's, said he was relieved the teenager had escaped.
He said the family had lived in the neighborhood at least a decade. Dondre skateboarded and played soccer with kids in the neighborhood, and "kept himself out of trouble," Elias said, but his mother didn't like some of his friends.
"She looked very angry a lot of the time - just angry," said Elias, clenching his jaw and staring ahead to demonstrate "how she was most of the time." He added, "I don't know what made her so mad."
(The Associated Press contributed to this report)