Ahem. From the Utah Election Code...
20A-1-502. Midterm vacancies in office of United States representative or senator.
(2) (a) When a vacancy occurs in the office of U.S. senator, it shall be filled for the unexpired term at the next regular general election.
(b) The governor shall appoint a person to serve as U.S. senator until the vacancy is filled by election from one of three persons nominated by the state central committee of the same political party as the prior officeholder.
http://le.utah.gov/~code/TITLE20A/htm/20A01018.htm