Officials acknowledged that doctors, nurses and others at the first hospital the man checked into, NewYork-Presbyterian Lawrence Hospital in Bronxville, might have been exposed to the illness.
“We believe that a couple of the medical professionals have been quarantined,” Mr. Latimer, the county executive, said.
Westchester County health officials were scrambling to trace his movements in the days before his hospital admission. The Westchester health commissioner ordered the synagogue, Young Israel of New Rochelle, to halt all services, and ordered the congregants who attended a bat mitzvah and a funeral there to self-quarantine.
In New York City, investigators with the health department interviewed colleagues at the man’s law firm on East 42nd Street, and identified seven people there worthy of some level of monitoring to see if symptoms develop.
The man has four children, two of whom flew back from Israel in recent days. But the younger two have links to New York City. One child, a daughter, attends a Jewish high school in the Riverdale neighborhood in the Bronx, and the school, SAR, which stands for Salanter Akiba Riverdale and describes itself as a Modern Orthodox Jewish day school, closed on Tuesday as a precaution.
The other, a college student, attends Yeshiva University but had not been on campus since Feb. 27, according to a statement released by the school. City officials said the man’s son, the Yeshiva University student, exhibited light symptoms that could be the coronavirus, or perhaps nothing at all.