Police got the case Wednesday morning after they say Baez and her husband brought the infant to Good Samaritan Hospital in East Islip, claiming she had fallen off a swing.
Police say doctors quickly discovered the truth.
Officers determined the suspect had shaken her niece at home in order to get the baby to stop crying.
The baby suffered subdural intracranial and retinal hemorrhaging. She was listed in critical condition.
The news is nothing short of astonishing to Baez's neighbors.
"It's a nightmare. It's a nightmare for something like that to happen," Donna Clavin said.
Neighbors say the family moved in here only about a month ago.
As we arrived at the house, a man pulled out of the driveway refusing to say a word about the allegations that would turn the stomach of any parent.
Baez has been charged with Reckless Assault of a Child.