Court proceedings are typically public in Colorado. In many cases, that includes divorce cases. Unless the court you go to determines that the case can be placed under seal, your divorce will be open to public record. There are some exceptions to open court records, of course. That may include protecting divorce records due to sexual abuse, for example.
When you or your ex want to seal the record, it's normal for at least one of you to ask, if not both. If you don't, the record is likely to be left open. Making the decision is up to you, but the judge may determine if the request will be granted or not. The court must decide if the party will be damaged more by an open record instead of a closed record. Normally, there is a presumption that court records are open to public scrutiny.