Colorado law states that January 1st is the assessment date. The owner of the property (as of January 1st) is considered the owner for that entire assessment year. If a property changes ownership during the year it is up to the buyer and seller to prorate the taxes.
Neither the Assessor nor the Treasurer is involved in or responsible for this process. It is also the responsibility of the taxpayer to notify the Assessor and the Treasurer when a business changes ownership. If a business closes after the January 1st assessment date, the taxpayer is also responsible for the entire year and for notifying the Assessor and Treasurer of the closure.