GREENWICH — The Nathaniel Witherell, the town-owned nursing center, reported its first case of the coronavirus on Tuesday — and it may not be the only case.

A patient in the short-term rehabilitation section of the facility has been diagnosed with the virus and was moved to Greenwich Hospital for treatment, said Larry Simon, chair of Witherell’s board of directors.

Other residents of the Witherell have shown some symptoms of the coronavirus, but their test results were not back yet, Simon said on Tuesday.

“Had this patient been in the long-term care part it could have been far worse,” Simon said. “Our greatest fear and something we need to address is the cross-contamination that can come from health care workers working in multiple facilities. …

“That is a real problem, and we need to revisit that. It’s a struggle here,” he said.

The news of the first case of the coronavirus came on the same day that the Nathaniel Witherell announced it had hired John Mastronardi as the facility’s new executive director.

For more on him and the future of the Nathaniel Witherll, click here.