The new rule was announced Tuesday. It was drafted after the April 16 massacre at Virginia Tech that left 32 victims and the gunman dead.
University officials also cited the separate arrests of three students at the Boulder campus for threats or implied threats in the days following the Virginia Tech shootings.
The new policy says Boulder campus officials "may refer individuals accused of making threats of violence for an assessment of the likelihood that they will act on a threat of violence."
A free-speech watchdog group called the Foundation for Individual Rights in Education says the policy could make people hesitant to speak freely despite First Amendment protections.
CU spokesman Bronson Hilliard says the policy was meant to keep the campus safe while protecting free-speech rights.
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