To 泓水入丹青: in some states you have to pay the fine 1st

by the deadline and then appeal by mail later. Don't know if that is the case in Colorado, but I know that's how some states handle it.

In many states, you have to either plead guity or fight in court. If you plead guity, it is highly likely the judge will reduce your fine by at least 50% and give you the option to go to driving school to wipe out the point (especially if you have had multiple points in a short period and worry about insurance).

If you plead not guilty, you would then have to appear in court (or have someone represent you in court if you can't appear yourself) and pray the cop who wrote the ticket won't have time to appear in court. If the cop does not show, it's a given you win. If the cop shows up in court, it will be very difficult for you to win. And if you lose, you pay the full amount plus court fees.