Cat-dog hybrids are not known to exist. Science Daily says that hybrids usually occur between species of different genera or subspecies. Hybrids between different families are extremely rare. Dogs come from the family Canidae, while cats come from the family Felidae.
While cats and dogs are not known to breed with each other, canines and felines have been known to interbreed within their family. Domestic cats have bred with Asian leopard cats, resulting in the semi-domestic Bengal. Similarly, domestic dogs have bred with wild coyotes, resulting in offspring known as coydogs or dogotes. Hybrids such as coydogs have a higher rate of sterility than non-hybrids, so most known specimens are first-generation hybrids.