I’m not addressing CSI, as they are not in high demand. It seems like everybody wants to be one. That job requires extensive education and training, especially in the sciences, and it would take pages to dispel the myths perpetuated by fictional television programs. You are not going to walk into your average agency and get hired for CSI.
A growing career sector is intelligence. Almost all federal agencies have intelligence personnel, as do many big police and sheriff's departments and state agencies. Intelligence usually requires specialized college training and is more likely to be a daytime, Monday to Friday type job. Fluency in a needed foreign language is a highly sought after skill. In some cases, the duties are more "tactical" in nature, often being more of an investigative assistant on major cases. In other cases it involves issues related to homeland security, terrorism, gangs, major drug dealing organizations, etc. The intelligence professional must put together the big picture. They establish the links and broad overview of terrorist, criminal or drug organizations. These can include international groups, gangs, and biker groups involved in illegal activity. They must understand the complexities of these organizations and what makes them tick. In some cases it is described as trying to drink water out of a fire hose--lots of information coming in that the analyst must then digest and make sense of and then give the collated summary to the investigator, director or via training to the troops. It is an excellent and rewarding career that is in high demand. The best intelligence training to qualify for this career may be by first serving in the military in an intelligence capacity.
There are other positions, such as clerical, that support law enforcement but dispatch, CSO and intelligence are among the more popular choices. The pay, benefits and rewards are very good. Hours and stress may be difficult for some, and exact duties will differ with the agency.