Pet owners beware: the coronavirus can infect your non-human companions, too.

“Two pet cats in New York state have tested positive for the coronavirus, marking the first confirmed cases in companion animals in the United States,” the Associated Press reported on Wednesday, citing federal officials.

Both cats, in households in different parts of the state, suffered “mild respiratory illnesses” and are expected to recover. One cat’s owner did test positive for the virus; the other had been ill, but wasn’t tested.

The Centers for Disease Control hastened to say that it appears to be a one-way path: there’s no evidence pet animals can pass the virus to people.

“We don’t want people to panic. We don’t want people to be afraid of pets” or to rush to test them en masse, said Dr. Casey Barton Behravesh of the CDC.

Still, the agency recommends that people “prevent their pets from interacting with people or animals outside their homes — by keeping cats indoors and dogs out of dog parks, for instance,” the AP says.

There have been a few reports outside the U.S. of pet dogs or cats becoming infected after close contact with contagious people, and a tiger at the Bronx Zoo in New York City also tested positive. Six other big cats — tigers and lions — showed symptoms, but all are recovering.