Various aspects of brain organization differ between the left and right hemispheres. Clues to the developmental origins of these asymmetries may be gained through associations with situs inversus totalis (SIT), a rare condition in which visceral organs are reversed on the left-right axis. In the largest previous brain imaging analyses of SIT (38 cases, 38 controls from Belgium), typical functional asymmetries such as left-hemisphere language dominance were mostly unaltered, but various aspects of asymmetrical cerebral structure - petalia, bending, and posterior venous anatomy – were often reversed in this condition. SIT can be a monogenic trait that arises from rare genetic variants, usually affecting motile cilia which help to create the embryonic left-right body axis. However, most SIT cases do not have obvious genetic causes and may arise from environmental or random effects during embryogenesis. We sequenced the genomes of 23 SIT cases and 23 controls from the Belgian brain imaging dataset and pooled with prior data from 15 cases and 15 controls. We aimed to discover whether there are altered brain asymmetries in SIT cases with disruptive DNA variants in ciliary genes, or in other types of genes, as compared to genetically unsolved cases. In total, 19 cases had likely causal variants affecting ciliary function, while 19 cases remained genetically unsolved. Functional and structural brain asymmetries were not significantly different in genetically solved versus unsolved SIT cases. Therefore, functional brain asymmetries seem largely independent of known mechanisms of visceral situs formation, while structural brain torque is altered in SIT regardless of the presence or absence of overt genetic causes.