cat nap - a short sleep
I'm going to have a cat nap while you're cooking dinner.
cat's got one's tongue - said about someone who doesn't speak (usually due to shyness)
It looks like the cat's got your tongue, Lucy. Are you always this quiet?
copy cat - a person who does the same thing as someone else
My sister is such a copy cat. First she bought the same car as me, and now she's applying to my school.
a cat on a hot tin roof - full of lively activity
The boy was jumping around like a cat on a hot tin roof and we could not make him be quiet.
fight like cats and dogs - to argue and fight with someone (usually used for people who know each other)
The two children were fighting like cats and dogs when we entered the room.