Agents from the Federal Bureau of Investigation have contacted lawyers for Mr. Cuomo’s aides, interviewed senior officials from the state Health Department and subpoenaed Mr. Cuomo’s office for documents related to the disclosure of data last year, the people said.

The interviews have included questions about information New York State submitted last year to the Justice Department, which had asked the state for data on Covid-19 cases and deaths in nursing homes, according to the people. False statements in such a submission could constitute a crime.

In some cases, agents traveled to the homes of state health officials to interview them about the data. In others, they spoke to officials by phone, according to the people, who requested anonymity to discuss the active investigation.