Kelly said Dmitriy Kanarikov, 35, of Brooklyn, had not been allowed to take his son Kirill alone since the breakup with his wife. He was allowed to do so for the first time on Sunday.
Police said he was supposed to turn over his son to his estranged wife at a police precinct. Instead, he threw his toddler off the roof of the building, police said.
Officers responding to an emergency call on the Upper West Side around noon Sunday found Kanarikov and the boy on the lower rooftops of two separate nearby buildings.
Kanarikov was pronounced dead at the scene, and his son was pronounced dead at a hospital, police said.
The boy's mother had custody of the child, and Kanarikov had visitation rights, authorities said.
Luis Ortiz told the New York Post that he was at the hospital when paramedics rushed the boy there and that they were pumping his chest and working on him.
"You could tell he was slipping away. They said the father was up there, but they didn't bring anyone else in. It was just heartbreaking. I have two kids of my own. They tried to do the best they could," Ortiz told the newspaper.
Ortiz told the New York Daily News that the tot was dressed in Christmas pajamas.
Authorities said the father did not live in the building listed as South Park Tower, which is a short distance away from Columbus Circle and Lincoln Center.
Police investigating the deaths left the building in the mid-afternoon to photograph a gray Lexus RX350 parked nearby.
It's the second time this year that a parent and child have been involved in a fatal plunge from a New York apartment building.
In March, a woman clutching her baby son in her arms plunged eight stories out of a Harlem apartment window to her death, but the 10-month-old survived. Authorities found a suicide note in her home.
Associated Press writer Tom McElroy contributed to this report.