Situs inversus (SI), a left-right mirror reversal of the visceral organs, can occur with recessive Primary Ciliary Dyskinesia (PCD). However, most people with SI do not have PCD, and the etiology of their condition remains poorly studied. We sequenced the genomes of 15 people with SI, of which six had PCD, as well as 15 controls. Subjects with non-PCD SI in this sample had an elevated rate of left-handedness (five out of nine), which suggested possible developmental mechanisms linking brain and body laterality. The six SI subjects with PCD all had likely recessive mutations in genes already known to cause PCD. Two non-PCD SI cases also had recessive mutations in known PCD genes, suggesting reduced penetrance for PCD in some SI cases. One non-PCD SI case had recessive mutations in PKD1L1, and another in CFAP52 (also known as WDR16). Both of these genes have previously been linked to SI without PCD. However, five of the nine non-PCD SI cases, including three of the left-handers in this dataset, had no obvious monogenic basis for their condition. Environmental influences, or possible random effects in early development, must be considered.