It is illegal to shoot a cat or a dog. The only exception to this is in an emergency for a dangerous dog or a severely injured dog or cat who is suffering and cannot otherwise be aided. In New York, the police and societies for the prevention of cruelty to animals (SPCA) have the authority to enforce the animal cruelty laws. If you provide me with the county, I will see if I can give you any further information. The difficulty in some of these cases is proving that the person actually made the statement (he might deny it) and proving that the person alleged to have killed the cat actually did so. 

I am so sorry to hear about your dog’s health problems. New York’s pet sale law states that the pet dealer must provide the purchaser with a statement indicating all of the following: “(1) The dog has no known disease or illness;  (2) The dog has no known congenital or hereditary condition that adversely affects the health of the dog at the time of the sale; or  (ii) A record of any known congenital or hereditary condition, disease or illness that adversely affects the health of the dog at the time of sale, along  with  a  statement  signed by a licensed veterinarian that authorizes the sale of the dog, recommends necessary treatment, if  any, and  verifies  that  the condition, disease, or illness does not require  hospitalization or nonelective surgical procedures, and is not likely to   require  hospitalization or nonelective  surgical  procedures in the future. …The statement shall be valid for fourteen business days following examination of the dog by the veterinarian.” The law further states that “For animals eighteen months of age or older, such examination shall include a diagnosis of any congenital conditions that  adversely  affect the health of the animal” and “No pet dealer shall knowingly sell any animal eighteen months of age or older that has a diagnosed congenital condition that  adversely affects the health of the animal without first informing the consumer, in writing, of such condition.” The pet sale law also provides consumers with certain remedies (including right of reimbursement of veterinary costs to treat the animal up to what was paid for the animal) if the purchaser gets a veterinarian’s certification that the animal was unfit for purchase within 14 days from the date of purchase. Given the time constraints mentioned above, the pet sale law will probably not help you. However, consumers are not limited by the pet sale law. Under the Uniform Commercial Code, merchants (this includes pet stores) could be held accountable to consumers if the merchant sells goods (this includes animals) that are unmerchantable (basically unfit for sale). You can file a complaint with the New York Attorney General’s Office and/or sue. In New York you can sue for up to $5000 in Small Claims Court. I don’t know how a court would decide your case but you might very well need an expert (such as a veterinarian) to testify on your behalf to improve your chances of winning the case. Next time, please consider adopting a homeless animal from a shelter.