The virus that causes COVID-19 is mainly spread from person to person, but it can also spread from person to animal. According to the U.S. Centers for Disease Control and Prevention (CDC), there have been cases of cats contracting COVID-19. But this mostly happened after animals were exposed to COVID-19 patients. But as far as the transmission of the COVID-19 virus is concerned, there is no evidence that the virus can be transmitted to humans or other animals through the skin or fur of cats.