If the recount is triggered due to a vote differential of less than or equal to 0.5% between any election item winner and any election item loser, the entity (State, County, Municipality, etc.) that certified the ballot measure is responsible for the fees (Colorado Revised Statute § 1-10.5-101(1)(b)).
If the recount comes at the request of an interested party, the interested party is responsible for the expense of the recount provided the results of the recount do not change the outcome of the election. If the recount does reverse the outcome of the election, or if the recount shows that a recount should have automatically been triggered, the cost of the recount will be refunded to the interested party (Colorado Revised Statute § 1-10.5-106(2)).