According to the East Baton Rouge Sheiff’s Office, deputies received a domestic disturbance call about 8:30 a.m. Monday.
The man, who identity has not yet been released, was taken into custody and the woman left with the child.
A neighbor reported Monday night that the woman, who name also is withheld, wandered into her yard, acting incoherently.
About 2 a.m., a relative of the woman called to say she was concerned about the infant. At that point, both parents were in custody.
A search later Tuesday turned up the baby’s body in a wooded area directly across from the house where the incident began Monday.