What I have heard in explanation of the proverb is in line with Mohan and Dr.Rao. Some people have a self made belief that they are not observed by anyone and can get away with anything they want to do- illegal a/or immoral. However the reality is that there will be some witness though that may not come immediately.
Cat is taken as examples for the dexterity, lack of loyalty and not hesitating to do wrong to those who nurtured it.
The other sayings related to cat ( in English and/or in other languages ) have their core meaning as given below:
However you throw, a cat falls on all four
Cat has nine lives
Cat prays , let all in the family become blind (so that it can steal milk)
What is the place for a cat at goldsmithy.
Cat's sleep( not getting deep sleep, but only small naps)
Walks like a cat( walks without making any sound- intention to do something secret)
Was like a cat, did n't imagine he/she could do that.( an otherwise usually quiet person doing something generally unwelcome )