Merely residing on the property for six months is not sufficient to create ownership in the home. Of course, depending on the facts of your case, if you transferred an interest in the home to them or made a written arrangement, then it is possible that they has an interest in the home. Some examples would be a executing a deed, whether or not it was recorded, lease-to-own, or option to purchase. Finally in certain circumstances equitable rights can be created in property, which means that even though no formal agreement exists a party still has a beneficial ownership in the property.

Nevertheless, it sounds more likely from the facts you describe that your friend is a tenant on your property, regardless if there is a formal lease agreement in place. This might be the case even if they haven't been paying rent.

In Colorado, once your friend is a tenant you can't force them to leave by using self help methods. For example, you can't change the locks or throw all of their possession on the street. Instead, you would have to formally evict them, which usually involves giving them a notice to quit and then going to court if they refuse to leave.

Considering that they are claiming an interest in your home I would recommend speaking with an attorney to fully discuss your situation. As I eluded to, the status of a tenant, trespasser, or owner can be complex and is highly factual.