Whereas the majority of studies regarding upper limb asymmetries in motor performance have focused on preferred arm dominance for producing motor output, studies exploring the role of sensory feedback have suggested that the preferred and non-preferred arms are specialized for different aspects of movement. A recent study by Goble et al. (2006) found evidence of a non-preferred left arm (and presumably right hemisphere) proprioceptive dominance for a target matching task that required subjects to both memorize and transfer across hemispheres proprioceptive target information. This paradigm contrasted previous studies of proprioceptive matching asymmetry that explored only memory-based matching and produced equivocal results. The purpose of the present study, therefore, was to examine task-dependent asymmetries in proprioceptive matching performance, including differences related to active versus passive presentation of the matching target. It was found that the non-preferred left arm of right handers matched target elbow angles more accurately than the preferred arm, but only in the matching condition that required both memory and interhemispheric transfer. Task-dependent asymmetries were not affected by the mode of target presentation and assessment of matching kinematics revealed differences in strategy for both the speed and smoothness of targeted movements. Taken together, these results suggest that the non-preferred arm/hemisphere system is specialized for the processing of movement-related proprioceptive feedback.