Higher rates of non-right-handedness (i.e. left- and mixed-handedness) have been reported in schizophrenia and have been a centrepiece for theories of anomalous lateralization in this disorder. We investigated whether non-right-handedness is (i) more prevalent in patients as compared with unaffected siblings and healthy unrelated control participants; (ii) familial; (iii) associated with disproportionately poorer neurocognition; and (iv) associated with grey matter volume asymmetries. We examined 1445 participants (375 patients with schizophrenia, 502 unaffected siblings and 568 unrelated controls) using the Edinburgh Handedness Inventory, a battery of neuropsychological tasks and structural magnetic resonance imaging data. Patients displayed a leftward shift in Edinburgh Handedness Inventory laterality quotient scores as compared with both their unaffected siblings and unrelated controls, but this finding disappeared when sex was added to the model. Moreover, there was no evidence of increased familial risk for non-right-handedness. Non-right-handedness was not associated with disproportionate neurocognitive disadvantage or with grey matter volume asymmetries in the frontal pole, lateral occipital pole or temporal pole. Non-right-handedness was associated with a significant reduction in left asymmetry in the superior temporal gyrus in both patients and controls. Our data neither provide strong support for 'atypical' handedness as a schizophrenia risk-associated heritable phenotype nor that it is associated with poorer neurocognition or anomalous cerebral asymmetries.