The murder trial of an Alberta woman accused of drowning her young sons has begun, two years after the two were found dead by their father in the bathtub of their Millet home.

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Curtis and Allyson McConnell are shown with sons Connor and Jayden in an undated photo. ((Facebook))

Crown prosecutor Gordon Hatch told the court the case is not one of who, what, where or when, but of why. The case will come down to Court of Queen's Bench Justice Michelle Crighton deciding Allyson McConnell's state of mind when she drowned her two children, he said.

McConnell, 33, is charged with second-degree murder in the deaths of 10-month-old Jayden and Connor, 2. Their bodies were found by their father, Curtis McConnell, in the bathtub of their Millet home, 40 kilometres south of Edmonton, on Feb. 1, 2010.

On Monday morning, the accused, wearing a grey suit and looking solemn but alert, entered a not-guilty plea shortly after entering the Wetaskiwin courtroom.

Accused under suicide watch

Her lawyer, Peter Royal, told the court McConnell suffers from "significant depression" and needs to be under a constant suicide watch.

'She then jumped over the edge, falling into the eastbound lanes of Whitemud Drive' —Agreed statement of facts

McConnell's mother, sister and grandmother sat on one side of the courtroom, while her former husband's father and sister sat on the other.

Curtis McConnell was not in the courtroom. He is scheduled to testify sometime this week.

The boys were last seen alive Jan, 29, 2010, when they went with others to a swimming play date in nearby Leduc, said Hatch. That night, McConnell tried to give away a number of items, including car seats, a computer and cameras, he said.

According to an agreed statement of facts, McConnell tried to commit suicide in the home after drowning the boys. She then drove to Edmonton, parking at the southside Toys "R" Us store and walking to the Delta Hotel to order lunch.

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A sheriff's van brings Allyson McConnell to the Westaskiwin courthouse. (CBC)

"She became emotional during her time at the hotel, so she left and walked back to the overpass where Calgary Trail passes over Whitemud Drive," the statement said. "She then jumped over the edge, falling into the eastbound lanes of Whitemud Drive."

McConnell fractured her collarbone, legs and pelvis.

Internet searches

Photos submitted as evidence suggest this wasn't her first suicide attempt. Police found electrical appliances submerged in a bathtub full of water. Alcohol and pill bottles were strewn across the floor and a rope was tied to a ceiling joist in the basement.

A forensic computer analyst testified that police found internet searches on the hard drive of McConnell's computer asking "How long does it take to drown?" and "How long does it take to die from strangulation?" Another search looked for information on how long it takes a person to overdose on sleeping pills.

The McConnells were separated and were involved in a custody battle, with Allyson angry at her husband for taking steps to ensure she could not return home to Australia, Hatch said.

McConnell wanted to move back to Australia with the boys, but their father refused. Three months before their deaths, a judge ruled the boys had to stay in Canada for the time being.

Curtis McConnell is expected to testify on Tuesday.

Allyson McConnell is being held at Alberta Hospital, a psychiatric facility in Edmonton.

With files from Janice Johnston and Briar Stewart