Her death was initially believed to be accidental, but Beckett was charged with her murder one year later.
The Crown has alleged Beckett killed his wife out of greed, hoping to cash in on life insurance and accidental death payouts.
In the statement played in court, Beckett told police his wife's drowning was an accident.
"I was sitting with my back to her and she was sitting with her front to me, I think," Beckett told Constable Jennifer Perrault.
"The last I can remember, she said that her back was sore. And then, all of a sudden, there's a splash. I think she stood up to stretch her back."
Beckett told the investigator she had taken off her life jacket because she felt hot.
He described her as "a fair-weather sailor" who does not swim.
"She was still holding the umbrella and she fell over the side," he said.
"The umbrella was over the other side. She kind of went down the side of the boat."
Beckett said he could see his wife drifting further away from him in the water.
"Then I spun the boat around to look for her and I could see her under the water. I went over the side of the boat, but I couldn't get down far enough."
In the statement, Beckett said Letts-Beckett was 15 to 20 feet beneath the surface.
"I could see her, but I couldn't just, couldn't reach her. So, I went to shore and got a rock and swam out, but I couldn't find her then. Then I saw some bubbles."
Beckett said he used the rock to get far enough underwater to grab his wife by the hand and pull her to the surface. "As I was swimming to shore, I was blowing air into her lungs, into her mouth, trying to do CPR," he said.
After performing chest compressions on shore, Beckett said, he swam out to retrieve his boat and tried unsuccessfully to lift his wife on board.
He said he then decided to drive to a nearby pontoon boat to ask for help.
John Saharchuk told court he drove his pontoon boat to where Beckett said he left his wife.
After attempting further CPR, Beckett and Saharchuk loaded Letts-Beckett's body into the pontoon boat and returned to the Shelter Bay campsite.
On shore, Saharchuk said, an off-duty paramedic confirmed Letts-Beckett was dead.
Beckett's trial is expected to last three months.