The boy, Devalon Armsrong, reportedly killed Viloude Louis by testing out World Wrestling Entertainment moves he had seen on TV.
Police say Armstrong murdered his half-sister.
"We express our heartfelt condolences. Authorities have already charged the accused with second-degree murder and determined that this was not an accidental death due to a wrestling move," the WWE statement said.
"The facts of this case clearly point to a lack of parental supervision and a teenager who had a history of violent behavior toward his 5-year-old stepsister.
"It is illogical to conclude that the repeated, brutal and ultimately fatal beating of a 5-year-old little girl by a teenager could be confused with imitation of WWE action seen on TV."
Armstrong, called 911 to report that his sister was not breathing, and that her stomach hurt. When ambulance personnel arrived, they found Louis unresponsive on the bathroom floor. They transported her to the hospital, where doctors were unable to revive her.
Armstrong confessed to deputies that he had used moves he had seen in the WWE ring. The girl had broken ribs, lacerations to her liver and internal bleeding, according to her autopsy.
The teen said "he knows wrestling on television was fake" and "appeared to enjoy talking about the wrestling moves and physical abuse," the police statement said.
The sheriff's office said Armstrong picked Louis up and repeatedly slammed her on the bed, punched her in the stomach and jumped on her, landing on his elbow like WWE wrestlers do on TV.
“There’s no explaining this kind of stuff when you’re slamming a five-year old over your knee and on your bed, and things of that nature," said sheriff Newell Normand. "They’re fragile. Five years old is still very, very young. "
Armstrong was arrested the day of the incident on suspicion of second-degree murder. He is being held in a juvenile detention center.
The children's mother does not face charges. She was at a nearby store during the incident and left the two at home alone.
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