(CNN) -

While protesters in Ferguson, Missouri, are demanding justice for the killing of Michael Brown by police, questions are being asked about the man who at the moment is responsible for pursuing any prosecution and whether he can be impartial.

Some residents and community leaders contend St. Louis County Prosecuting Attorney Robert McCulloch has deep ties to the police and has favored law enforcement in criminal cases.

Missouri State Sen. Jamilah Nasheed launched a petition that now has more than 26,000 signatures to remove McCulloch from the case and replace him with a special prosecutor to handle any criminal case arising from the August 9 shooting of Brown, an African-American who was unarmed when killed by a white police officer.

The shooting has touched off demonstrations that have led to confrontations with police, and some looting and violence.

The National Guard was called in, President Barack Obama appealed for "understanding" and cooler heads, and Attorney General Eric Holder visited Ferguson on Wednesday to assess things. His agency has launched a civil rights probe.

McCulloch, however, has indicated that he is going nowhere and plans to do his job.

CNN has sought to interview him, but the request has not been granted.

But in a radio interview with with McGraw Millhaven on KTRS, McCulloch promised a comprehensive and fair investigation.

"We will be presenting absolutely everything to this grand jury. Every statement that a witness made, every witness, every photograph, every piece of physical evidence. Absolutely nothing will be left out so the grand jury is making their decision based upon absolutely everything and we'll go from there," McCulloch said Wednesday.

The grand jury will be given evidence as early as Wednesday, a process that could last until the middle of October, McCulloch said.

Critics question McCulloch's dedication to a fair outcome and some have said he has moved too slowly.

The officer "should be charged and arrested. It's been over a week now," Patricia Bynes, the Democratic Party committeewoman for Ferguson Township, told CNN. We are "motivated to have a transparent case that's accountable to the community and to make sure justice is done at every level," Bynes said.

Bynes said McCulloch's ties with police in the county could cloud his judgment.

McCulloch's father was a police officer and was killed on the job in 1964 by an African-American man, when McCulloch was 12, McCulloch's spokesperson Ed Magee confirmed to CNN. In addition to his father, McCulloch's brother, an uncle and a cousin all served with the St. Louis Police Department, and his mother worked as a clerk at the department, Magee said.

McCulloch, who as a teenager lost a leg to cancer, made it his career ambition to become a prosecutor. He was quoted by the St. Louis Post-Dispatch as telling a reporter, while first campaigning for the office: "I couldn't become a policeman, so being county prosecutor is the next best thing."

McCulloch has no plans to step aside and Magee said it doesn't have any impact on how he will handle the current case.

"I have absolutely no intention of walking away from duties and the responsibilities entrusted in me by the people of this community," McCulloch said during the radio interview.

While the Justice Department is conducting its own civil rights investigation, Ferguson elected officials are concerned about the local investigation. McCulloch has overseen controversial cases before, some including police officers and black suspects.

The petition being circulated points to a 2000 incident in which two suspected drug dealers were killed by two police officers, McCulloch never brought charges against the officers, concluding they acted in self-defense. A subsequent federal investigation found that the men were unarmed and not moving in the direction of the officers, but because the officers felt endangered, the investigation found that the shootings were justified, the St. Louis Post-Dispatch reported.

"He doesn't have the fortitude to do the right thing when it comes to prosecuting police officers," Nasheed said on CNN's "Newsroom" on Tuesday.

Chris King, editorial director at the St. Louis American, an African-American publication, said McCulloch has already "manipulated" the Brown case by the way he is releasing information. The St. Louis County Police released a convenience store video from just minutes before Brown's death that showed a person who resembled Brown stealing a box of cigars.

"All of this information should have come out all at once in group. By leaking out in pieces, he is encouraging this kind of speculation," King said on CNN's "New Day."

Concerns about McCulloch arose again after Missouri Gov. Jay Nixon replaced the St. Louis County Police with the Missouri State Highway Patrol for security last week because he said the initial law enforcement response to the shooting was excessive. McCulloch told CNN affiliate KMOV that the governor had "no legal authority" to make such a move.

Why no arrest yet?

Upsetting to Ferguson residents, Missouri State Sen. Maria Chappelle-Nadal said, is that Darren Wilson, who has been identified as the officer who shot Brown, has not yet been arrested or charged. He is on paid administrative leave. It is up to the grand jury to determine what charges, if any, will be placed on Wilson.