The teenager, whose name has not been released, was shot in the neck this week in an incident in Arapaho County that left Davidson, his wife and 3-year-old daughter dead.
The Rocky Mountain News Friday said the girl told deputies that Davidson had convinced her stepmother and two siblings to accompany him to their old house in the town of Bennett on Thursday by telling them her had presents for them and planned to turn himself in.
During the ride, Davidson allegedly pulled a gun from a duffel bag and opened fire when they got to the house.
The Denver Post said the girl ducked in the back seat to avoid a bullet fired at her head. She was able to run to a nearby home for help, but Davidson's wife and daughter were killed before Davidson took his own life. An infant in the car was unharmed.
The shootings took place a few days after Davidson escaped from a minimum-security prison where he was serving a sentence for fraud in connection with a massive Internet spamming operation.
The newspaper said he contacted his family a few days later and asked to see them before he surrendered to authorities.