Final election counts in Pitkin, Garfield and Rio Blanco counties on Monday showed Beeson trailing Democratic challenger Sherry Caloia.
Caloia's margin of victory is more than 100 more than the amount that would have required an automatic recount, which means Beeson will have to pay for the recount cost unless the results change the race's outcome.
Beeson is hoping he has enough leftover campaign funds to cover the cost.
(Copyright 2012 by The Associated Press. All Rights Reserved.)