Tybalt is the pet black cat in the Lowood family. Like most children, Tybalt can see and hear things that are already dead.
Tybalt is an unruly thing, and it doesn't care much for anyone other than Cas' mother. It has a weird habit of pulling all the hair off it's tail and leaving little tuffs of black over the house.
Tybalt has been in the family since before Cas' father died, and has moved from place to place with the family as their four-legged ghost hunter of sorts. Tybalt is loved dearly by Cas' mother, but gets very little to no attention from Cas himself, instead opting for violence.
Tybalt ends up being killed in the attic by the Obeahman nearing the end of the first book.