A police spokesman said that three people died and another was injured in the crash. He said it was unclear whether the helicopter was hit by gunfire or whether it came down because it veered into a radio antenna.
Television images showed the helicopter engulfed in flames on the roof of the kindergarten, with dense black smoke pouring out. Witnesses said the infants had gone home just before the crash occurred.
"As of now we have three dead," Heriberto Zazueta, a spokesman at the city's public security department, said.
Alerted to a bank robbery at a branch of the Banpais, the helicopter was chasing a station wagon around 10 men in it when theys opened fire, he said.
He said the police did not fire back as the vehicle raced through narrow streets in a heavily populated suburb just east of the city centre. The helicopter came down near one of the city's main traffic arteries.
The pilot, Vicente Rodarte, was flown to a nearby hospital with serious burns and other injuries. The dead were a high-ranking police official, another officer and a police radio operator, Mr Zazueta added.