Schizotypy is a multidimensional personality construct representing the extension of psychosis-like traits into the general population. Schizotypy has been associated with attenuated expressions of many of the same neuropsychological abnormalities as schizophrenia, including atypical pattern of functional hemispheric asymmetry. Unfortunately, the previous literature on links between schizotypy and hemispheric asymmetry is inconsistent with some research indicating that elevated schizotypy is associated with relative right over left hemisphere shifts, left over right hemisphere shifts, bilateral impairments, or with no hemispheric differences at all. This inconsistency may result from different methodologies, scales, and / or sex proportions between studies. In a within-participant design, we tested for the four possible links between laterality and schizotypy by comparing the relationship between two common self-report measures of multidimensional schizotypy (the O-LIFE questionnaire, and two Chapman scales, magical ideation and physical anhedonia) and performance in two computerized lateralised hemifield paradigms (lexical decision, chimeric face processing) in 80 men and 79 women. Results for the two scales and two tasks did not unequivocally support any of the four possible links. We discuss the possibilities that a link between schizotypy and laterality 1) exists, but is subtle, probably fluctuating, unable to be assessed by traditional methodologies used here; 2) does not exist, or 3) is indirect, mediated by other factors (e.g. stress-responsiveness, handedness, drug use) whose influences need further exploration.