Background: Structural brain changes and cognitive impairments have been identified as indicators of genetic risk for schizophrenia. However, the pattern of associations between such structural and functional liability markers has been less well investigated. Methods: Magnetic resonance imaging data and cognitive assessments were acquired in 31 patients with psychosis, 32 non-psychotic first-degree relatives and 28 controls. The relationship between cerebral grey matter density and cognitive performance was examined using computational morphometry. Results: Two out of 6 cognitive tests revealed significant associations with grey matter density in regions of the frontal lobe, basal ganglia, thalamus and cerebellum in patients and relatives. In patients, poorer executive functioning was associated with cerebellar grey matter density deficits. In relatives, poorer executive functioning was associated with increased grey matter density in the cerebellum and frontal lobe. In both patients and relatives, strategic retrieval from semantic memory was positively associated with grey matter density in basal ganglia structures. Some additional negative associations in the patients differentiated this group from relatives. Conclusions: The overlap in structure-function relationships in individuals with schizophrenia and those with liability for the disorder may suggest that regional grey matter density alterations functionally alter particular neurocircuits, which could lead to cognitive deficits. The non-overlapping structure-function correlations may reflect disease-related or compensatory mechanisms.