My question involves an eviction in the state of: Colorado

I let a family member move in with me when he/she had no where else to go in the beginning of August. The unwritten agreement was that he/she would move out by the holidays when he/she got back on their feet. After he/she moved in it became clear that he/she's version of getting back on their feet involved sponging off of me. So I told him/her in the middle of December that I wanted him/her moved out by 31 January. He/she are now creating a hostile situation as we are getting closer to 31 January...I was/am getting fed up with this so I told him/her they needed to leave ASAP. He/She then called the cops and claimed that I was harassing them. The cops didn't buy the situation that he/she laid out but informed me that I needed to follow the eviction process because it was clear that he/she was not going to leave freely. So I've been reading up on the process but I'm confused because the vast majority of the information deals with paying tenants. I don't want rent or anything...I just want him/her out. I'm leaning towards the Notice to Quit route but even that seems unclear because the description of that process discusses the "lease." What's the best way to handle this situation using the eviction process in Colorado?