Does the paper names "Certificate of no marriage record" exist in Denver Colorado, USA? If yes, how to get it? Much appreciate.

You need to talk to the Clerk and Recorder's office to see what sort of paperwork they can give you.

I am not sure anyone can give you what you are looking for. There is no statewide repository of marriage records. Every County Clerk and Recorder keeps his/her own set of records for that county. In addition, Colorado recognizes common law marriage, for which there would not be any kind of official record. So, at least in Colorado, the absence of a document acknowledging that your are married does not mean that you are not legally married.

Are you in contact with the other party? Any attorney could draft an affidavit for the two of you to sign that states you are not currently, and have not ever been , married. If you both sign it and have it notarized, then it would be valid. However, there are no court forms, and I don't believe there's any way for any county or state clerk to create anything saying that you aren't married in Colorado.