Carnegie Mellon is not very strict when it comes to people using its facilities, as those who don't go to CMU are free to use the library, academic buildings, student center, and workout facilities (although there is a fee) within normal daytime hours. CMU is very strict, however, when it comes to cheating, plagiarism, and illegal downloads. Teachers and teaching assistants are usually responsible for dealing with suspected cheating and plagiarism, although the higher-up deans can get involved. If a student is even suspected of cheating, teachers have been known to assign R's (an F, basically) and extra assignments to punish the student. This doesn't happen often because of how strictly enforced the academic policies are.
CMU makes up for its iron-fist academic strictness with a looser, more accommodating campus police. While CMU students might make fun of campus police from time to time, they really have some of the most flexible policies that still offer students safety from both themselves and others. Campus police really only intervene if a student is caught participating in illegal activity, but they won't go looking for it. For example, students who decide to congregate in dorm rooms with a 30 pack of Natty Light and a cheap bottle of vodka won't be disturbed unless it is extremely obvious that they are drinking, where the RA is required to call the campus police. Usually, if the RA knocks on the door and this is happening, or if people are stupid enough to walk the halls holding alcohol, the RA will simply make them pour it out. On campus, things are pretty lax, but you should start to use caution when going to off-campus parties, as then the Pittsburgh police are the first to respond, and they usually aren't so accommodating.