A mutation in hox genes causes cervical ribs in mammals (and more than one gene can be involved according to a research article I read). Hox genes control the body plan along the head-tail axis (basically segmentation) from fruit flies to humans. And humans have 39 pairs of these genes. These genes are also expressed in the nervous system, abdominal, and vascular tissues too. Mutations in the hox genes also contribute to limb formation. So it is entirely possible that other birth defects accompany cervical ribs since these genes are so important in development.