New York City voters believe by a 2-1 margin that the mayor's spouse should not have a chief of staff, and most don't think the first lady should have a major policy role, according to a Quinnipiac University poll.

The survey was completed just as Rachel Noerdlinger, first lady Chirlane McCray's top aide, announced she will take an unpaid leave of absence. Noerdlinger announced Monday she was stepping away for an indefinite period amid scrutiny over her teenage son's arrest last week on trespassing charges, the criminal history of her boyfriend and her failure to disclose in a city background check that she lives with him, along with omissions of financial details.

McCray, who is chair of the Mayor's Fund to Advance New York City and who Mayor Bill de Blasio has repeatedly called his closest adviser, should have no role in shaping public policy, according to 34 percent of voters surveyed.

Only 24 percent say she should have a "major role" and 37 percent say she should have a "minor role," the poll found.

The poll, conducted from Nov. 12 through Monday via landline and cellphone, surveyed 1,164 voters and has a margin of error of plus or minus 2.9 percentage points.

"Mayor Bill de Blasio is making his job a family affair, and voters aren't enthusiastic," said Quinnipiac assistant poll director Maurice Carroll.

Additionally, the poll showed NYPD Commissioner William Bratton has a 47 percent job approval rating, the lowest for the city's top cop in 13 years. Commissioner Bernard Kerik was at 46 percent in May 2001. Bratton predecessor Ray Kelly had the highest recent rating with 75 percent in January 2013.

Majorities of voters say that the NYPD is generally tougher on blacks than whites and that there was "no excuse" for the July death of Eric Garner, a black Staten Island man placed in an apparent chokehold by an officer. Also, 86 percent believe that crime is a very serious or somewhat serious problem and 73 percent say police brutality is a very serious or somewhat serious problem.

Noerdlinger is a former communications adviser to the Rev. Al Sharpton, who spoke about her and her son Khari, 17, during an unrelated news conference Wednesday.

"Ironically, about eight months ago," Sharpton said unprompted, "there was a reporter running, trying to prove, I was Khari's father." He said he was not.

Noerdlinger further debunked the claim. "I met Rev. Al Sharpton in January 1999 for the first time," she said in a statement. "Khari Noerdlinger was born on Dec. 20, 1996."

Mayoral spokeswoman Rebecca Katz defended McCray's work for the city, including "her efforts to combat domestic violence to her mental health advocacy to her pivotal role as a leading spokeswoman for universal pre-K."

The NYPD did not respond to requests for comment on Bratton's poll numbers.

With Anthony M. DeStefano