Imitation is a potentially crucial aspect of social cognitive development. Although deficits in imitation ability have been widely demonstrated in autism spectrum disorder (ASD), the specificity and significance of the findings is unclear, due largely to methodological limitations. We developed a novel assessment of imitation ability, using objective movement parameters (path length and action duration) derived from a touch-sensitive tablet laptop during drawing actions on an identical tablet. By direct comparison of the kinematics of a model's actions with those of the participant who observed them, measures of imitation accuracy were obtained. By replaying the end-point of the movement as a spot on the screen, imitation accuracy was compared against a “ghost control” condition, with no human actor but only the end-point of the movement seen [object movement reenactment (OMR)]. Hence, demands of the control task were closely matched to the experimental task with respect to motor, memory, and attentional abilities. Adolescents with ASD showed poorer accuracy for copying object size and action duration on both the imitation and OMR tasks, but were significantly more impaired for imitation of object size. Our results provide evidence that some of the imitation deficit in ASD is specific to a self-other mapping problem, and cannot be explained by general factors such as memory, spatial reasoning, motor control, or attention, nor related to the social demands of the testing situation.