Bentley was among four officers who confronted Dziekanski at Vancouver's airport on Oct. 14, 2007, when the Polish immigrant was repeatedly stunned with a Taser and died.
He was found not guilty last year. The other three officers also charged with perjury are still awaiting trial.
The Crown's theory was that the officers worked together the night of Dziekanski's death to concoct a story to tell investigators and then lied at the public inquiry to cover up their collusion.
But the judge said there were other reasonable explanations for what Bentley said, both in his statement to homicide investigators and during his testimony at the inquiry. He concluded the Crown failed to prove Bentley lied at any point.
The Crown appealed, and in recently filed court documents, prosecutors argue there was ample evidence to prove the officers colluded. Prosecutors contend the judge failed to properly consider the evidence and apply the law.
"The trial judge committed three significant errors in his approach to the evidence that the RCMP officers had collaborated," says the Crown's written arguments, filed earlier this month.
"Had the trial judge correctly approached the issue of collaboration and considered all of the relevant evidence on this point ... there is a reasonable possibility that the respondent might not have been acquitted."
The documents say the judge incorrectly focused on whether there was evidence of collusion before the public inquiry in 2009, even though the Crown's theory was that the officers actually collaborated on the night of Dziekanski's death.
Prosecutors also argue the judge failed to apply the correct legal test when determining whether the officers colluded, and they say the judge failed to consider the motive that the officers would have had to justify their deadly use of force.
During the trial, the Crown did not produce any direct evidence showing the officers collaborated on the night of Dziekanski's death, such as a witness who might have seen them huddled together at the airport.
Instead, the Crown relied almost entirely on comparing the four officers' police notes and statements. Prosecutors argued "strikingly" similar errors contained in all four officers' notes and statements proved they must have collaborated.
For example, all four Mounties said Dziekanski was physically forced to the ground, even though the video clearly shows he fell on his own after the first jolt of the Taser.
Bentley's defence lawyer, Peter Wilson, argued during the trial that his client did the best he could to recall a fast-paced, stressful situation. Wilson said Bentley and the other officers simply had no opportunity to work on a story that night, and he noted other civilian witnesses made similar errors in their own statements.
Wilson declined to comment on Tuesday.
No date has been set to hear the appeal.
Bentley was called to the airport along with Const. Kwesi Millington, Const. Gerry Rundel and former corporal Benjamin (Monty) Robinson.
Dziekanski, who spoke no English and had been at the airport for nearly 10 hours, had been seen throwing furniture in the international arrivals terminal.
Within seconds of arriving, the officers surrounded Dziekanski, and Millington fired his Taser.
The officers all testified at a public inquiry in early 2009, each telling the inquiry Dziekanski posed a threat when he picked up a stapler, and they were charged with perjury two years later.
At a pre-trial hearing for Millington in March, the Crown revealed a new witness who is expected to testify at Millington's trial.
The court heard Janice Norgard, who is the former common-law spouse of Bentley's cousin, is expected to say the four officers met privately at her house in the lead-up to the inquiry.
Prosecutors indicated they intend to allege Millington and the other officers met to co-ordinate their stories as they prepared to appear at the inquiry.
The three officers who have yet to stand trial have all pleaded not guilty, and none of them have had a formal opportunity to respond to Norgard's alleged evidence.
Norgard's evidence is not mentioned in the documents filed by the Crown in the Bentley case.
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