Mount Vernon Detective Sgt. Rob Scott said Tuesday that the 11-day-old baby was pronounced dead last Thursday.
The mother was carrying the baby in a harness in the front of her with the baby facing her chest during an outing in the Bronx, he said.
The mother wrapped the baby in a blanket and then zippered up her coat over the child.
When they reached their Mount Vernon home, Scott said the baby was not breathing. Paramedics were unable to revive her.
Scott said the grandmother had legal custody of the baby girl, but he did not know why. The family's name was not made public.
No charges were filed. Police said it's just a terrible tragedy.