The official -- speaking on condition of anonymity as he wasn't authorized to discuss the event -- earlier said all four people in the helicopter had escaped alive, but later said two of those aboard had died.
The pilot and another surviving officer aboard suffered burns.
Television images showed the blackened wreckage of the chopper in the middle of the football field.
Police were not able to say if this was the first time one of their helicopters had been shot down.
The helicopter crashed about five miles (eight kilometers) southwest of one of Rio's 2016 Olympic zones will be located. The city won the Olympic bid earlier this month despite concerns about security.
Intense fire fights between rival drug gangs broke out shortly after midnight in the Macacos slum as one gang tried to seize a rival's territory.
Police moved into the area in the early morning, though gunfire continued.
The spokesman said three bodies were found in a vehicle in the slum, though it was not clear if they were involved in the shootouts.
Violence also broke out Saturday in the Jacarezinho neighborhood, where a commuter bus was set on fire. Police did not have details of that event, though gangs sometimes set buses aflame to protest police operations.
Despite increased policing efforts, Rio remains one of the world's most dangerous cities. The violence generally is contained within slum areas, though it sometimes spills into richer neighborhoods nearby.
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