Deputies said the accident occurred Friday, when the baby's father somehow fell while carrying the baby.
The boy was identified as Lemuel Kelly IV, who was born last December. The father was identified as 25-year-old Lemuel Kelly III.
Neighbors said the parents were doing CPR when emergency crews arrived.
The infant died Friday night at Cape Fear Valley Medical Center.
According to the Harnett County Sheriff's Office, deputies responded to a reported injured infant at 45 B Shady Street shortly before 3 p.m. Friday. Anderson Creek EMS and Harnett County EMS responded and transported the baby, who had suffered a head injury, to the hospital.
Lemuel Kelly III told authorities that he had tripped when he was walking into the apartment and had dropped the infant as he fell.
The mother was at work at the time of the incident.
The infant's body was sent to North Carolina Medical Examiner's Office in Chapel Hill for an autopsy.
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