It's a chain of five steps. First, the County Assessor sets the actual value of your property (roughly what it would sell for, on a state-defined valuation cycle). Second, the State of Colorado sets an assessment rate — a percentage that differs for residential versus non-residential property and that the legislature and ballot measures have changed repeatedly. Third, actual value times the assessment rate gives your assessed value. Fourth, each taxing district your property sits in (county, town, school, fire, library, metro or special districts) sets a mill levy; one mill is one dollar of tax per one thousand dollars of assessed value, and the levies of every overlapping district are added together.
Fifth, assessed value times the total mill levy (divided by 1,000) is your tax bill. Because the assessment rate and the mill levies both change and vary by location, pull the current numbers from the Routt County Assessor and Treasurer before you rely on any estimate.