The skull was quite large in proportion to the rest of its body. It measures in length in the "C. nasicornis" holotype, measured from the tip of the snout to the , which connects to the first cervical vertebra. The width of this skull is difficult to reconstruct, as it is heavily distorted, and Gilmore's 1920 reconstruction was later found to be too wide. The fairly complete skull of specimen MWC 1 was estimated to have been in length and in width; this skull was somewhat more elongated than that of the holotype. The back of the skull was more lightly built than in some other larger theropods due to extensive skull openings, yet the jaws were deep to support the proportionally large teeth. The lacrimal bone formed not only the back margin of the antorbital fenestra, a large opening between eye and , but also part of its upper margin, unlike in members of the related Abelisauridae. The quadrate bone, which was connected to the lower jaw at its bottom end to form the jaw joint, was inclined so that the jaw joint was displaced backwards in relation to the occipital condyle. This also led to a broadening of the base of the lateral temporal fenestra, a large opening behind the eyes.