In the manga, Utena's relationship with Anthy is only that of friendship and it's hinted she has feelings for Touga. In the movie, Utena went to Ohtori to find Touga after the two apparently broke up.
Utena's bond with Anthy in the manga is described as a friendship, although it is implied that she might be romantically interested in Touga. Similarly, in the movie, Utena travels to Ohtori to find Touga, who appears to have ended their relationship.