Fossilized in animals = mummified in humans.
Wrong. Any animal can be mummified, artificially or naturally--I've seen mummified cats in Egypt, and scientists have found at least one mummified mammoth. In mummies, the original tissue is still present.
Generally, fossilization occurs when the original tissue has been replaced by minerals--turned to rock, basically. It is possible for an animal to be naturally mummified and then fossilized, but it's not necessary.
What doesn't exist is a fossilized cat (or human), or a mummified (but not fossilized) dinosaur.