If you've been investigating crimes on the police force, you're already armed with many of the skills you need to become a private investigator (PI). In fact, companies look for PIs who already have some law enforcement training. In most states, you'll also need to be licensed to practice as a PI.
Being a private investigator in the real world is nowhere near as glamorous as it's portrayed on TV. For the most part, you're not going to be hot on the trail of a team of international jewel thieves. Instead, you'll probably be following cheating spouses on behalf of their suspicious wives, tracking down identity thieves or perpetrators of insurance fraud, or looking for missing persons. You'll be doing a lot of tedious grunt work, like digging through tax filings, legal documents, motor vehicle records and other boring documents. You may also do surveillance, which can involve sitting in your car and looking through a pair of binoculars for hours at a time.
The upside to working as a private investigator is that you can work anywhere, and generally you can choose your own hours. If you're hired by a large security firm, you'll be dealing with bigger issues -- like corporate investigations -- but you'll also have to work a set schedule.