Although bathing and washing are forbidden on Yom Kippur, Kohanim may wash their hands in preparation for Birkat Kohanim, as is normally done throughout the year. Since this washing is done for Halachic reasons, and not for comfort or enjoyment, it is permissible, and the Kohanim may wash the entire hand until the wrist, as they normally do. This is the ruling of the majority of the Halachic authorities, including Rav Haim Palachi (Turkey, 1788-1869), in his work Moíed Leíkol Hai (18:3), and Hacham Bension Abba Shaul (Israel, 1923-1998).
However, Hacham Bension adds that whereas generally Kohanim wash each hand three times in preparation for Birkat Kohanim, on Yom Kippur they should wash each hand only once. Since the additional two washings are not technically required, they should not be done on Yom Kippur.
Some Leviyim have the practice of washing their hands before washing the Kohanimís hands in preparation for Birkat Kohanim. Hacham Bension writes that a Levi who normally follows that practice may wash his hands on Yom Kippur, as well. Quite obviously, a Levi who normally does not make a point of washing his hands before washing the Kohanimís hands should not do so on Yom Kippur.
Summary: Kohanim may wash their hands until the wrist in preparation for Birkat Kohanim on Yom Kippur, but they should wash each hand only once, and not three times. A Levi who normally washes his hands before washing the Kohanimís hands may do so on Yom Kippur, as well.