The most commonly used Colorado background check resource is the state Bureau of Investigation. They can issue limited criminal history records to anyone who makes a request. You can even get such records directly from their website, and there is a small fee for each search (you'll need a credit card). Because it is an open records state, there are no restrictions on who can have access. Information obtained online is not considered official, and you can contact the Bureau by mail to get an official record on CBI letterhead for an additional fee.
Other Record Sources
Though criminal records are freely distributed, other types of records are more restricted. Even so, there are some other Colorado background check resources you can use. The Department of Public Health can issue copies of birth, death, marriage and divorce records to anyone who is a relative of the person on record for example.