MONTREAL -- Quebec has ordered an independent inquiry into what led to the wrongful arrest of Mamadi III Fara Camara, but it's not clear that it will include the possibility he was racially profiled.

Public Security Minister Genevieve Guilbault said that there's only a possibility that aspect could be included in the investigation and that she doesn't want to mandate the issues the independent inquiry will look into.

She said, however, racial profiling could be an element, but that it will be up to Justice Louis Dionne who was formally named as the head of the investigation Wednesday.

"Mr. Dionne has all latitude and independence to address any issue that he considers relevant in his investigation," said Guilbault. "We don't want to involve ourselves in the way that he should conduct his investigation. It is very important that we have the most independent and competent person to conduct this investigation and I think we have it."

The inquiry will investigate Camara's arrest and the charges against him.

The 31-year old PhD student was put in jail for six days before being released and completely cleared.

It happened after a police officer was assaulted during a traffic stop.

Camara's lawyer said they are considering suing Montreal for that wrongful arrest and detention.

The inquiry will take 5 months to complete and Guilbault has promised it will be made public as long it does not contain confidential information.

This morning Quebec's opposition parties said there is no question racial profiling should be included in this investigation.

"It needs to talk about racial profiling," said Quebec solidaire (QS) public security critic Alexandre Leduc. "It's a big issue in the police institution in Quebec and Montreal. I guess, even the CAQ government recognizes it."

Questions remain about Dionne's neutrality.

The Crown prosecutor's office said it would like to participate in the inquiry, and justice Dionne's last role was as the director of that office.

Some politicians raised concerns about a potential conflict of interest.

Guilbault said Dionne left the Crown prosecutor's office in 2011 so would likely not personally know any of the people he will investigate when looking at how the Crown found enough evidence to charge Camara.