According to the CDC:
There is no reason to think that any animals including pets in the United States might be a source of infection with this new coronavirus. To date, CDC has not received any reports of pets or other animals becoming sick with COVID-19. At this time, there is no evidence that companion animals including pets can spread COVID-19. However, since animals can spread other diseases to people, it’s always a good idea to wash your hands after being around animals.
Update April 22, 2020: While two cats have tested positive for COVID-19 in New York, health officials explain that “while some animals can become infected by people, there’s so far little evidence that animals are transmitting the disease to humans.”
Update April 28, 2020: While a NC pug has become the first US dog to test positive for COVID-19, the CDC shares that there is “no evidence that animals play a significant role in spreading the virus.”