cherbare seamons answered 5/2/2007 I Have A 3 Month Old Female Shih Tzu And She Has Been Eating Out Of My Cat's Litter Box. Is This Normal And What Do I Need To Do? I have a 3 year old shit zu and she did the same not long ago. Keep the litter box away or get rid of the cat, or just figure a way to deal with the bad breath.