Birth certificate images for 1917 are now online at archives.utah.gov/digital/81443.htm. Although they are not indexed by name yet, if one knows the birth date and county it should not be difficult to locate the correct folder and browse through a few images for the time being. Free saving and printing of images is available.
Birth certificates are the permanent legal record of all live births in the state filed with the Utah Office of Vital Records and Statistics. The information recorded includes the newborn child’s full name, sex, date of birth, place of birth, whether a single or multiple births took place, the parents’ names, race (color), ages, birthplaces, occupations, and marital status, and the number of children born to the mother.
Certificates from 1905 to 1910 have been indexed, with 1911 to 1917 available to browse online.