What causes arthritis in the scull?

No such thing: The skull is a solid bone (series of bones that are fused together) that does not have any joints. There is a joint at the base of the skull that connect it to the first vertebra in the spine - and that can develop arthritis at the "atlanto-occipital joint" Most common cause is degenerative arthritis

The skull has no joints and does not develop arthritis. Perhaps you are thinking of neck pain which can be muscular or skeletal. Both have a multiplicity of causes.