The current race and ethnicity data available from Census Bureau products uses the race and ethnicity groups as classified by the U.S. Office of Management and Budget (OMB) in 1992. While race and ethnicity are self-identified traits in the decennial census and the American Community Survey, the OMB categories limit respondents to five racial groups and one ethnicity (Hispanic or Latino). The five racial groups are: White, Black or African America, American Indian and Alaska Native, Asian, and Native Hawaiian and Pacific Islander. For anyone identifying with a different race, they are grouped as Some Other Race.
Estimates of the population by Race and Ethnicity from the U.S. Census Bureau can be found here: State and County
The Utah Population Committee also produces estimates of race and Hispanic or Latino origin at the county and state level.
Historical data on race and Hispanic or Latino origin in Utah can be found in this document: Utah Minorities: The Story Told by 150 Years of Census Data