CHICAGO (CBS) — A Cook County judge has agreed to appoint a special prosecutor to handle the murder case against Chicago police officer Jason Van Dyke, charged in the fatal shooting of 17-year-old Laquan McDonald.

Judge Vincent Gaughan granted the request for a special prosecutor nearly a month after Cook County State’s Attorney Anita Alvarez asked to be recused from the case.

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Alvarez had initially resisted calls for a special prosecutor, declining her office had any conflict of interest, and defending her handling of the case. However, she reversed course more than a month after losing her bid for re-election in the Democratic primary in March.

Gaughan said he will first contact Illinois Attorney General Lisa Madigan’s office to ask if they can take over the prosecution. If her office does not take the case, Gaughan will contact the state’s appellate prosecutor’s office, and then other state’s attorneys in Illinois. If none of them can take the case, Gaughan said he would reach out to private attorneys.

G. Flint Taylor, one of several civil rights attorneys who asked Gaughan to appoint a special prosecutor in the McDonald case, said they asked the judge to consider naming a “blue ribbon team” of attorneys they recommended to be the special prosecutor.

While Taylor would not name anyone on the list, he said it includes African Americans and others who are former judges and former federal prosecutors with no connection to the Cook County State’s Attorney’s office.

Two petitions had been filed seeking to replace Alvarez in the case, citing her close ties to the Fraternal Order of Police, the union that represents Chicago police officers. One petition was filed by a group of civil rights attorneys and activists, the other was filed by Rev. Jesse Jackson.

Critics have said Alvarez is beholden to the police union, and has failed to adequately prosecute cases of police misconduct and corruption.

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Meantime, Gaughan said he would hold off on a decision whether to appoint a special prosecutor to investigate if other officers at the scene the night McDonald was shot and killed tried to cover up what happened.

“This is not yet shovel-ready,” he said.

Gaughan said no grand jury is investigating other officers who were at the scene, and federal prosecutors haven’t said if they’re looking into that possibility.

Attorney Locke Bowman, who joined Taylor in seeking a special prosecutor in the McDonald case, said it’s disappointing a grand jury is not investigating any possible cover-up attempt, and he said that’s all the more reason Gaughan should appoint a special prosecutor to do so.

“We can all see that there’s a potential for criminal charges against these other officers. As a city, we’ve been waiting for the Police Department, the criminal justice authorities to take charge of this matter and address it,” Bowman said.

Gaughan said he might reconsider the issue on July 1.

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Defense attorney Dan Herbert said he’s prepared to take the case to trial, no matter who the prosecutors might be.