I've rarely seen anything more then a year of criminal justice required to become an officer or civilian police department employee. I honestly think a full criminal justice degree is one of the most useless degrees out there.
You should be aware that "CSI" as depicted on TV is pure fiction. They show individuals performing multiple tasks that are accomplished by a team in the real world. The jobs shown done by super investigators on CSI are actually divided among detectives, crime scene techs, and multiple crime lab personnel.
The Forensic science degree is for people who want to work in a lab. Natural sciences like chemistry and biology also provide the needed curriculum. Many labs also do crime scene call out and provide assistance to the detectives/police, but not all labs and not all personnel at a lab do crime scenes. If you want to work in a lab, a master's degree would be very helpful as the popularity of the job right now has made for lots of competition. Most people who work in a crime lab often end up running toxicology samples which is highly repetitive. The people who test physical evidence (ballistics, DNA, trace, etc.) have a lot more variation, but it still isn't as exciting as what is depicted on TV.
The larger PD's often have their own crime scene processing people. They typically photograph crime scenes, dust for prints, occasionally analyze the prints, identify and gather evidence for the crime lab personnel to analyze, and create crime scene diagrams. The crime scene techs for police departments often do move into the position laterally from being an officer or from a civilian post like dispatcher, meter maid, records tech, or manning the public info desk. Every PD has a different requirement. The officers themselves usually fulfill this role in smaller PD's. Cops don't usually need college degrees and rarely do the crime scene techs need anything more then a two year degree (and often not even that much is required).