Struck by an out-of-control driver fleeing the police, a 4-year-old girl lay dying on an Upper West Side sidewalk in early June. Officers immediately radioed for an ambulance, and one arrived about eight minutes later — an eternity to those waiting on the street. The girl, Ariel Russo, was declared dead at the hospital less than an hour later.

Blame quickly spread, with much of it directed at the city’s 911 emergency network.

Other episodes began to surface. Calls to the 911 system generated conflicting addresses for dispatchers; screens appeared to indicate that information had been lost; an unacceptably long response time to a fire in the Bronx was recorded.

Unions for emergency workers questioned whether New Yorkers were now less safe because of the mistakes. It was not human error, they said, but a gross indictment of the city’s $2 billion overhaul of the aging 911 computer network.

“They wanted it to be the system, because it feeds into this perception that the whole 911 system is a mess, that unified call taking doesn’t work, and on and on,” said Caswell F. Holloway, the deputy mayor for operations who is overseeing the project. “That is not the case.”