The Crown is appealing to have the manslaughter conviction of Allyson McConnell, an Alberta woman who drowned her two sons in February 2010, changed to second-degree murder.
McConnell was convicted last month and is due to be sentenced on June 4.
The province will seek a new trial if it can't get the conviction upgrade.
The appeal was launched on grounds that legal errors were made in the analysis of the evidence, in the consideration of intent, and the application of reasonable doubt, said Jason Maloney, spokesman for Alberta Justice and Solicitor General.
McConnell drowned Connor, 2, and 10-month-old Jayden in the bathtub of their Millet, Alta., home during a bitter divorce battle with her husband Curtis McConnell.
Justice Michelle Crighton ruled that she had reasonable doubt about whether McConnell could form the intent to kill her sons, ages 10 months and two years.
During the trial, the prosecution argued McConnell killed her boys at the family home in Millet, Alta., as revenge against her husband, Curtis McConnell who had refused permission to let her return to her native Australia with the boys.
But the defence said McConnell's mind was so clouded by booze, sleeping pills and severe depression that she could not have formed the intent required to convict her of second-degree murder.
The Crown, seeking a conviction of second-degree murder, suggested the judge relied on the faulty opinion of an expert witness and misunderstood the effects of combining of sleeping pills and alcohol on the ability to form intent.
Manslaughter carries a penalty anywhere from probation to life in prison.
Second-degree murder carries an automatic life sentence with no chance of parole for 10 years.
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