Pitkin County District Judge James Boyd on Friday started choosing 12 jurors and four alternates. Prosecutors will then present evidence to the jurors about the deaths.
Parker and Caroline Lofgren of Denver and their two children, ages 8 and 10, were found dead the day after Thanksgiving in a home where they spending the holiday.
They had won a weekend at the vacation home in a fundraiser.
Investigators say a disconnected exhaust pipe in a utility closet was leaking carbon-monoxide gas.
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