SARS-CoV-2 (the virus that causes COVID-19) has been passed from people to cats, but NOT from cats to people.
More experiments are needed to assess the ability of SARS-CoV-2 to pass from cat to cat. At this stage one experiment showed that COVID-19 in one cat passed to another cat in the next cage, however, two other infected cats failed to pass the virus to the paired cat in the cages next to them.
Cats have rarely been infected with COVID-19 to date, one in Belgium that is questionable, and one confirmed in Hong Kong.
Tigers and lions in a zoo in the United States have shown respiratory signs with one tiger tested and being found positive to the virus. Infection has been seen in ferrets and dogs, so there is some transmission to animals possible, but appears to be rare.
A study out of China found that 15 out of 102 cats tested positive for antibodies which means that they had come into contact with the virus. Only 3 of these 15 were strongly positive for SARS-CoV-2 and these cats were owned by infected people.
Again, there is no evidence for cat to people transmission.
Always follow the government and health department guidelines and wash your hands thoroughly after handling your cats or litter trays.
Follow this link for the Chinese study: https://www.biorxiv.org/content/10.1101/2020.04.01.021196v1.full.pdf
Please note that this study has not been peer reviewed (assessed by experts in their field prior to being published).
Other coronaviruses infect cats and have been around for years and they do not affect people.