Two of Boston's elected officials this week praised police response to a Mattapan shooting that injured a baby, but pressed for more direct communication between officers and emergency response workers.

In a Tuesday hearing, Councillors Charles Yancey and Stephen Murphy questioned officials from the city's Emergency Response Services and other agencies on a June shooting on Fairlawn Avenue.

"We might have gotten trained medical personnel looking at the baby two three four minutes before they ultimately did," Murphy said.

Arriving on the scene, police officers wrapped the baby girl in a blanket and rushed her to Caritas Carney Hospital, afraid that a dispatched ambulance could not get to the crime scene in time.

A man reportedly had climbed up the balcony of the Mattapan apartment complex and fired through a sliding glass door, injuring both the father and the baby.

The officers' decision to transport the baby was "difficult decision and it was the right one," Murphy acknowledged.

"There needs to be an additional training component," he added. "If certain parameters are being met, a police officer should be able to bypass dispatch and go to the responding agency to get an estimated time of arrival. If that had happened, there wouldn't have been a four to five minute wait."

EMS officials said the case was "unusual" and the information that was coming in that night was conflicting and confusing, leading to a delay. Police were on the scene at 8:40 p.m., minutes after receiving the call. An EMS unit waited for police to arrive and ensure the house was safe. At 8:43 p.m., police reported serious injuries, at which point an ambulance was already en route for two minutes. At 8:48 p.m., police officers left with the baby in their car, just as the ambulance pulled in through a different area.

EMS officials said the channels used by police and emergency services are "too busy" for direct communication. "That's part of things we're going to work on with police," said Richard Serino, the EMS chief.

Yancey said he remained nervous over emergency services, since services remain stretched thin. "I don't leave here with a great deal of comfort," he told EMS officials.

Serino said they had assigned a deputy superintendent to the communications division between the two agencies to allow police to send more messages to dispatches. They also added eight ambulances since July to help with response time.