Gov. Kathy Hochul of New York cautioned residents on Tuesday evening about two major storm-related problems that were likely to linger after the system moved on: widespread power outages and the risk of flooding in certain parts of the state.

In an interview with Spectrum News, a cable television outlet, Ms. Hochul said that 52,000 New York households — most of them in the western part of the state — were without power after heavy winds knocked out power lines. She predicted the numbers would rise through the night — and she was right. By 10 p.m., the number had nearly tripled, to about 143,000, according to data from the site poweroutage.com.

Restoring power was no simple matter, she added, because the trucks needed to make repairs could not operate while gusts remained fierce.

“We’re asking families look out for each other, check on neighbors,” Ms. Hochul said.

The governor said she was also “very concerned” about the threat of flooding, especially in the Hudson Valley, where a huge rainstorm over the summer swept away cars and killed one person.

“That’s what we’re facing, not just today, but over the next few days, with the melting snow and the four inches of rain that’s coming,” she said.

By 10 p.m., rainfall totals in and around New York City ranged from three-quarters of an inch to an inch and three-quarters on average, according to the National Weather Service. Similar totals had been recorded from the Catskills to the mid-Hudson Valley, with the highest total being about two inches in Rockland County.

Ms. Hochul’s advice to New Yorkers?

“We need people to please stay home,” she said, adding that “it doesn’t take much for your vehicle to be swept away. Even just a couple inches of rain can be treacherous.”