Allyson McConnell, 33, of Millet, Alberta, is charged with second-degree murder in the deaths of her sons Connor, 2, and Jayden, 10 months.
Prosecutor Gordon Hatch said it will be up to Court of Queen's Bench Justice Michelle Crighton to determine whether McConnell's state of mind at the time of the drownings warrants a murder conviction, the Canadian Broadcasting Corp. reported. She is being treated in a psychiatric facility in Edmonton.
McConnell's estranged husband, Curtis McConnell, who discovered the boys' bodies Feb. 1, 2010, is expected to testify Tuesday, the CBC said.
Allyson McConnell, who wore a gray suit when she entered a not-guilty plea Monday, suffers from "significant depression," her attorney, Peter Royal, told the court. She had tried to take her own life after drowning the boys and her lawyer said she is under constant suicide watch.
The couple had been separated and going through a custody battle prior to the drownings. Hatch said Allyson McConnell had been upset with her husband for blocking her desire to return home to Australia.
2014: The Year in Music [PHOTOS]