The black cat is a minor animal character from Halloween Town. He\she appeared during This is Halloween and Sally's Song. There is a possibility that he\she might be Sally's pet.
The cat looks very similar to the one seen in Tim Burton's first stop-motion film, Vincent. She/he is the only cat in this film. (Excluding background cats)
Cat during "Sally's Song"
Hiding in the trash can...
The black cat on Sally's lap