I am pretty sure Jo answered this in an interview somewhere. If not, my son Beorn is just more perceptive than I thought.
Beorn says Crookshanks is half kneazle, based on the entry in
Fantastic Beasts & Where to Find Them:
Kneazle
Ministry of Magic Classification: XXX
(Competant Wizard Should Cope)
The Kneazle was originally bred in Britain, though it is now expoprted worldwide. A small catlike creature with flecked, speckled, or spotted fur, outsize ears, and a tail like a lion's, the Kneazle is intelligent, independent, and occasionally agressive, though if it takes a liking to a witch or wizard, it makes an excellent pet. The Kneazle has an uncanny ability to detect unsavoury or suspicious characters and can be relied upon to guide its owner safely home if they are lost. Kneazles have up to eight kittens in a litter and can interbreed with cats. Licenses are required for ownerhip as (like Crups and Fwoopers) Kneazles are sufficiently unusual in appearance to attract Muggle interest.