But the commissioner is still perceived as more influential than Rev. Al Sharpton.
"Bratton has come in for a lot of criticism," said Maurice Carroll, assistant director of Quinnipiac University's polling service. "The rule is if police do something perceived as bad, the police commissioner's numbers go down."
According to the poll, 48 percent of voters approved of the way Bratton is doing his job versus 35 percent who disapprove. That's down from 57 percent who approved and 19 percent who disapproved in June.
The poll also showed that Sharpton is the most important black leader in the city.
"He's the leading black politician in New York until someone else comes along," said Carroll.
Asked who has more influence with de Blasio, Bratton or Sharpton, 54 percent said Bratton had more influence compared to 25 percent who thought it was Sharpton.
The civil rights activist has served as a spokesman for the family of Garner — a 43-year-old Staten Island man whose chokehold death was ruled a homicide by the medical examiner following a July 18 attempt to arrest him for allegedly selling loose cigarettes — and is also heavily involved in the case of Michael Brown, who was shot and killed by police in Ferguson, Mo.
Twenty percent of voters said Sharpton was the top black leader in New York City. That beat Rep. Charles Rangel, Public Advocate Letitia James and Brooklyn Borough President Eric Adams, who all receive between 1 to 3 percent.
"Having Sharpton be a prominent figure engaging with the African-American community after the incident has helped reinforce this image," said Basil Smikle, a political consultant.
Despite the Garner case, Mayor Bill de Blasio's approval ratings have held steady at 50 percent, virtually unchanged since June, with continued overwhelming approval ratings from black voters at 65 percent.
Only 36 percent of white voters approve of how de Blasio is handling his job versus 45 percent who disapprove.
"De Blasio's numbers say he's doing just what he did on election day which is so-so among white voters....and overwhelmingly well among black voters," Carroll said.
The much criticized relationship between Sharpton and de Blasio has a lot to do with that, said Smikle.
But voters did not agree that Sharpton had too much influence over de Blasio.
According to the poll, 30 percent of voters said Sharpton had too much sway with de Blasio while 39 percent said Sharpton's influence was just right. Another 10 percent though Sharpton had too little influence and 21 percent didn't know or didn't answer.
Forty-six percent of voters approve of de Blasio's handling of crime and 46 percent disapprove. That's down from 57 percent who approved of his handling of crime in June versus only 30 percent who disagreed.