If you came outside and found someone searching through your trash bin, you may be surprised and outraged. You may feel like your privacy had been violated. You'd think on one else had any right to know what you'd thrown away.
However, the police are legally allowed to search through your bins if they want. This is true with or without a warrant. Legally speaking, you give up your expectation of privacy the second you put the trash outside of your home, and then it's fair for law enforcement to take a look.
So, why do they want to look in the trash? If they're already investigating you, they could be looking for evidence that supports a theory—such as a receipt that shows you were near the crime scene at the time that it was carried out.
They could also be looking for evidence that could get them a warrant. If an officer has a hunch but no evidence, the police can't usually get a warrant just for baseless suspicion and then search your home. They need something more to go on, and the trash is one of the few places they can look without that warrant.
Naturally, it's worth noting that this doesn't kick in until you take the trash out of your house. If you throw something away in the garbage can under the sink, the police have no right -- in the vast majority of cases -- to look through that can without a warrant.
As this shows, it's incredibly important to know all of your rights and the protections you get from privacy laws in Colorado.
Source: FIndLaw, "Can Police Search Through Your Trash?," Brett Snider, accessed May 24, 2016