The inquiry is expected to begin in the next two months, which means it would likely take place at the same time as the ongoing criminal probe.
A $30-million lawsuit related to last month's collapse has also been launched that names the mall owner, the city and the provincial government.
There's no legal prohibition against it, but "issues can arise" when both an inquiry and a criminal probe proceed simultaneously, said Brendan Crawley, a spokesman for the Ontario Ministry of the Attorney General.
"As a result, the commissioner conducting the inquiry will typically take care to make sure that the inquiry does not interfere with other proceedings, including criminal or regulatory matters," he said in an email.
Inquiries proceeding alongside police probes have been affected by the criminal investigations in the past.
Lawyer Peter Wardle, who represented victims at the Ontario inquiry into the work of disgraced pathologist Charles Smith, said two inquiries in the 1990s were derailed due to concerns about fair trial rights when there were parallel criminal investigations.
In 1990, the Supreme Court of Canada shut down the Patti Starr inquiry in Ontario, which lawyers argued violated the rights of the individuals whose actions it was examining.
The court said that inquiry served as a "substitute police investigation" into a specific allegations of criminal conduct by Starr. They ruled that the inquiry exceeded the province's jurisdiction because the terms of reference were almost identical to the criminal charges.
"The Supreme Court of Canada did not hold that you couldn't have a criminal investigation and a public inquiry at the same time," said Ronald Foerster, who was a junior lawyer on the government side of that inquiry.
"You just couldn't have them at the same time if they were exactly the same."
An inquiry into the 1992 Westray mining disaster in Nova Scotia was also delayed due to concerns about the fair trial rights of senior Westray Coal employees.
A judge ruled that the inquiry was unconstitutional, but the decision was overturned in 1993 by the province's top court. However, it ruled that the inquiry could only continue once all charges went through the court system.
It's impossible to know whether the Elliot Lake inquiry will run into similar difficulties because its terms of reference have not yet been determined, Foerster said.
Doloris Perizzolo, 74, and Lucie Aylwin, 37, were killed and 20 others injured when a portion of the Algo Centre Mall roof caved-in June 23 and plummeted into the shopping centre.
Ontario Attorney General John Gerretsen said the inquiry — which was called before the Ontario Provincial Police announced their investigation — will probe the events leading up to the tragedy and review the emergency response to the disaster.
He said it may also raise questions about the role private owners play in maintaining their properties.
A prominent Ottawa judge, Justice Paul Belanger, will lead the inquiry. Usually, commissioners are directed not to make any conclusions or recommendations on criminal charges or civil liability.
"Presumably, they won't name any individuals and it will be much broader than any criminal act that may be involved," Foerster said.
If a person who's under investigation by police testifies at an inquiry, that evidence cannot be used against them in any future court proceeding, including a criminal trial, Foerster said.
"Having said all of that, the reality is that it is at a public inquiry, their testimony will go out there, so people will know about it," he said. "It's just that their specific words can't be used against them in a future trial."
It is possible for a potential juror in a future criminal trial to hear that evidence through media reports, he acknowledged. But they'll be instructed to disregard it at trial.
To avoid problems involving the right to a fair trial, an inquiry can wait until the criminal process is resolved — as was done in British Columbia in the Robert Pickton inquiry, Wardle said.
Cameron Ward, a lawyer who represented families of Pickton's victims, said most provincial administrative processes in B.C., such as inquiries and coroner's inquests are deferred until the criminal investigations are completed.
Commissioners can also hold portions of inquiries in private, which happened during the Maher Arar inquiry when matters of national security were involved, Foerster said.
During the Gomery Commission into the sponsorship scandal, retired Justice John Gomery ordered a ban on the publication of testimony of three men who faced criminal charges related to the sponsorship program.
There are ways that an inquiry could be held in private, but that decision is entirely up to the commissioner, Foerster said.
"While there are ways of doing it," he said. "It can — depending on the circumstances — be quite difficult to do."