The cerebral lateralization of written language has received very limited research attention in comparison to the wealth of studies on the cerebral lateralization of oral language. The purpose of the present study was to further our understanding of written language lateralization, by elucidating the relative contribution of language and motor functions. We compared written word generation with a task that has equivalent visuomotor demands but does not include language: the repeated drawing of symbols. We assessed cerebral laterality using functional transcranial Doppler ultrasound (fTCD), a non-invasive, perfusion-sensitive neuroimaging technique in 23 left- and 31 right-handed participants. Findings suggest that the linguistic aspect of written word generation recruited more left-hemispheric areas during writing, in right-handers compared to left-handers. This difference could be explained by greater variability in cerebral laterality patterns within left-handers or the possibility that the areas subserving language in left-handers are broader than in right-handers. Another explanation is that the attentional demands of the more novel symbol copying task (compared to writing) contributed more right-hemispheric activation in right-handers, but this could not be captured in left-handers due to ceiling effects. Future work could investigate such attentional demands using both simple and complex stimuli in the copying condition.