To determine whether wild Indo-Pacific bottlenose dolphins (Tursiops aduncus) at Mikura Island, Japan, show asymmetry of eye or flipper use during a social behaviour, we investigated the laterality of flipper-to-body (F–B) rubbing, in which one dolphin (“rubber”) rubs the body of another (“rubbee”) with its flipper. We analysed 382 episodes of video-recorded F–B rubbings performed by identified individuals (N = 111 rubbers). F–B rubbing was conducted significantly more frequently with the left flipper than with the right flipper. The duration of F–B rubbings was also significantly longer with the left flipper than with the right flipper. Of 20 dolphins, nine individuals showed significant left-side bias as the rubber in this behaviour, whereas no dolphins showed significant right-side bias. The results indicate a population-level left-side bias of the rubber in F–B rubbing. An analysis of the swimming configurations during this behaviour suggests that the asymmetry in F–B rubbing was caused not only by the laterality of the rubber, but by a preference for use of the left eye in both dolphins during this behaviour. Dolphins used the left eye significantly more frequently than the right eye during the inquisitive behaviour, while they showed no significant bias in flipper use during the object-carrying behaviour. These facts also suggest that the asymmetry of F–B rubbing is caused by the preference for using the left eye. Significant left-side bias was observed only in F–B rubbings initiated by the rubbee, in which the rubbee determined its position during this behaviour. This suggests that this behavioural asymmetry was enhanced by the rubbees choosing the left side of the rubber to ensure better and longer rubs.