Platt kidnapped the child and later told the police where to find the body. Police are calling it an "extremely hideous" murder.
Police Superintendent Warren Riley of New Orleans did not know the amount of child support that Platt had been ordered to pay. He would not reveal to the media how the little boy died. He did say the coroner would talk about it once the autopsy was completed.
Riley said the mother was in a safe place.
Platt, 22, had visiting rights but until Friday had never seen the child. On Saturday police put a notice out asking for people to look for the child. His father had said three men in dreadlocks and AK-47 rifles have kidnapped the boy before midnight Friday.
The Associated Press
"His story never really added up," Riley said. "He was a suspect from the very beginning."
Platt had a couple of minor arrests before he was arrested on Saturday.
"How does an individual — because he's ordered to pay child support to take care of a kid ... believe that this is so much pressure that he would face — he would do this hideous act to his own child, or to any child, and think that is a remedy to paying child support?" Riley said. "I mean there are some sick individuals in this society, and this gentleman is clearly one."