Liberal Leader Raj Sherman says it's important to know if current legislature members are being investigated as well.
If so, Sherman says, Premier Jim Prentice must ask them to leave the government caucus until the probe is complete.
"There have been far too many distractions from the proper business of governing. Albertans are tired of it. They have a right to expect laser focus from their MLAs on the issues that matter," he said in a news release Friday.
"If any current PC MLAs are under investigation by the RCMP, then the government cannot operate free from distraction."
NDP critic Deron Bilous, in an interview, said there still needs to be a public inquiry to determine what happened under Redford.
He noted that a criminal probe by its very nature looks at a narrower range of information compared with a public inquiry.
"There are going to be questions left unanswered because they just don't fit into an RCMP investigation," said Bilous. "(Information such as) which cabinet member knew what and didn't act on it, and who was implicated in this beyond Redford.
"It is possible we've got current sitting cabinet ministers who were implicated from months ago. Will we ever get to the bottom of this?"
A spokeswoman for the Alberta RCMP confirmed Friday that a review of an auditor general's report into Redford's spending has escalated into an investigation. Sgt. Josee Valiquette declined to divulge any other information.
"We're just confirming we're conducting an investigation at this time," she said.
Valiquette said Mounties began reviewing the case after the Justice Department forwarded them a copy in August of auditor general Merwan Saher's report into Redford's spending.
In the report, Saher said he found "Redford and her office used public resources inappropriately."
He cited Redford's use of government airplanes and her plan to convert public space atop the government's Federal Building into personal living quarters.
Saher said Redford and her staff used the planes for personal reasons and that the former premier's daughter sometimes flew alone on the planes without her.
He also found the flights were block-booked to give the appearance the aircraft was full so no other passengers could board.
Redford's travel disclosures contained reporting loopholes that allowed, for example, a trip to India and Switzerland earlier this year to come in at $131,000 when the true cost was $450,000, Saher said.
If there are any charges resulting from such investigations, they usually revolve around fraud or breach of trust.
Prentice, who took over as Progressive Conservative party leader and premier in September, has promised to sell the government air fleet and bring in new rules to prevent abuse of public money.
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