Yes, you can, but unless your cat was a very valuable purebreed, breeder, or winning show animal--and you can prove that fact--you will spend more on the lawsuit than you get back. Unfortunately, the law does not recognize or provide compensation for the animal's suffering or the pet parent's emotional loss: all you can recover for wrongful animal death is the economic value of the animal, which for many (e.g. shelter animals or rescues) is essentially zero.