The car veered and struck the pole when police tried to pull it over, Sgt Steve Martos said.
The girl and her brother, who had minor injuries, were both in their pajamas, Martos said.
The children's mother had put them to bed but couldn't find them a half-hour later. She called police to report her children may have been kidnapped.
The accident occurred a short distance from the children's home.
"It's just an unfortunate tragedy," Martos said.
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