Aspen police cited Armstrong with failing to report an accident and speeding on 12 January after the 28 December accident, but only after his girlfriend, Anna Hansen, admitted to lying for him.
Armstrong declined immediate comment, and his lawyer, Pamela Mackey, didn't immediately return a call.
Hansen initially told police she had been driving home from an Aspen Art Museum party when she lost control of Armstrong's GMC Yukon on the icy roads, hitting the cars.
She said she drove because "Lance had a little bit to drink," according to the reports.
A man who had been renting one of the damaged cars told a police detective that Hansen came running up to his house in high heels, apologising and promising to pay for the repairs.
"She said, 'I'm Anna, we're the Armstrongs, my husband's Lance, he was just driving maybe too fast around the corner or something'," the man told police, according to the reports.
He called 911 to report a hit-and-run. Hansen and Armstrong left the scene before police arrived.
Detectives later interviewed Hansen, who eventually told them Armstrong was driving, but they had both decided to let her take the blame.
"We've had our family name smeared over every paper in the world in the last couple of years and honestly, I've got teenagers, I just wanted to protect my family," Hansen told police.
"I thought, gosh, Anna Hansen hit some cars, it's not going to show up in the papers, but Lance Armstrong hit some cars, it's going to be a national story."
Hansen is not charged with a crime.