Does the state prohibit Approval Voting?

Alternative voting methods are not prohibited.

There are jurisdictions that choose more than one office.
Non partisan municipal and special district elections in which there are more than one at-large seat have featured instructions to vote for candidates equaling the number of seats available on a board. ie: “Vote for Five” or “Vote for no more than five.”
Some voters have seen multiple choice ballots. Candidates are asking for the voters approval to fill the available offices. They do not run for individual at-large seats. Boulder voters are familiar with this type of ballot.
This is not a defiance of state law, nor is it the establishment of home rule governance. There is simply no  statewide prohibition on methods.

Before 2008 it was possible for a local government to employ ranked voting. What was missing were the rules for a clerk to develop a “ballot plan”.
Each year the Secretary of State promulgates rules for clerks statewide concerning elections practices. After passage of any elections legislation the SoS is likely to promulgate new rules. The SoS may not accept a ballot plan that defies rules from his or her office. This is the sensible enforcement of rules in coordination with clerks. Clerks are not prohibited from using different voting methods, but may refuse to do so without guidelines.

Our Approval Voting Method bill asks for those guidelines. The use of Approval Voting is voluntary.

Jonathan Singer's Approval Voting bill HB17-1281 in 2017 was our last legislative attempt to instruct the Secretary of State to create rules and procedures for Approval Voting elections. Now in 2019 we are led to believe that the new administration of Jena Griswold has an interest in supporting alternative voting methods, including Approval Voting.
Local election supervisors in counties, cities/towns, and special districts need election rules from the Colorado Secretary of State.
Home Rule communities may already use Approval Voting without SoS rules, but find them valuable.
Approval Voting for Colorado seeks additional rules, not a change to existing rules.
Use of Approval Voting will be strictly voluntary by communities and districts that want to try it.