Cephalonomancy means divination using a head. It is likely this is a corrupt form of cephaleonomancy which is defined as divination by study of the shape of the skull or head, especially of a donkey. This was done by broiling the head on hot coals. The practicioner would mutter a few prayers or incantations, and then repeat names of suspects in a crime. If the jaws made any motion or the teeth chattered against one another, they had found the guilty party.
Rather than use a bed of coals, they might place a coal on an ass's head and say the names of those who were suspected of a crime. Crackling would be interpreted as a sign of guilt.
Germans and Lombards used the head of a goat rather than a donkey.