The Crown is requesting the 2011 jury decision be annulled and a new trial ordered.
The doctor from Saint-Jérôme, Que., admitted to the February 2009 fatal stabbing of Anne-Sophie, 3, and Olivier, 5, and was housed for 46 months in the Pinel Psychiatric Institute before being released last December.
The Crown argued that the killings were premeditated, intended as revenge against his former wife, Isabelle Gaston, who was having an affair.
- Isabelle Gaston welcomes appeal of Guy Turcotte's verdict
Turcotte's defence lawyers argued that he suffered from serious mental illness at the time and was intoxicated on windshield washer fluid as part of a suicide attempt.
The Crown believes the trial judge did not properly instruct jurors and claims the judge should have never offered the option of "not criminally responsible" for voluntary intoxication.
"You can’t plead 'I was intoxicated' by alcohol either," said criminal lawyer Robert LaHaye.
If the verdict is annulled and Turcotte found criminally responsible in a retrial, he would receive a mandatory life sentence, with no chance of parole for 25 years.