Two women died after they were swept away by floodwaters as a powerful storm battered the New York City area and parts of Connecticut, where at least 100 people were evacuated, officials said on Monday.

The storm system dumped nearly 10 inches of rain in some areas of southwestern Connecticut on Sunday, causing rivers to crest their banks and leading to a flash flood emergency declaration, officials said.

The two women who died were residents of Oxford, Conn. Their bodies were recovered in Little River, which runs through Oxford, on Monday, officials said during a news conference. Both had been trapped in vehicles and had tried to escape them only to be swept down the river.

Gov. Ned Lamont of Connecticut declared a state of emergency on Monday.

Among the scores of evacuations, officials made boat rescues at Kettletown State Park and Jackson Cove on Lake George, where more than 30 people were celebrating the birthday of a 2-year-old.

The same storm system also brought torrential rain and flash flooding to Long Island early Monday, forcing multiple rescues and briefly closing parts of major highways leading to New York City. The National Weather Service issued a rare flash flood emergency during the worst part of the storm, describing it as a “particularly dangerous situation.” A flash flood emergency is the highest level of flood warning.

In New York City, the downpour disrupted trains and forced the authorities to ground or cancel flights.

On Monday, more than 900,000 people in Suffolk County on Long Island were under a flash flood emergency that was scheduled to expire before dawn, but a warning was extended into the early afternoon.

Brian Ciemnecki, a meteorologist with the Weather Service in New York, said that it was rare to issue such an alert for the area and that weather officials made the initial call for the emergency after receiving numerous reports of water rescues and other damage caused by the storm.

The rain in most parts of Long Island had stopped by early Monday, he said, but he expected lingering issues such as potential road closures, especially in the north half of the island.

A flash flood warning had been in effect until 1:30 p.m. on Monday for a portion of southeast New York, including Suffolk County. Between six and 10 inches of rain had fallen in the affected area, officials said. The agency said early Monday that multiple rescues were ongoing in the Nesconset, Ronkonkoma, Smithtown and St. James areas on Long Island.

Suffolk County Executive Ed Romaine on Monday declared a state of emergency following the storm in hopes of getting assistance for affected homeowners and businesses.

“We are shocked at the amount of damage in Suffolk County,” Mr. Romaine said during a news conference on Monday. “The rain caused major flooding, mudslides, buried cars and damaged houses.”

He added that some roads “will be impassable for months.”

Among the damaged areas was a pond in Stony Brook that overflowed, leading to a collapse of Harbor Road.

Gloria Rocchio, the president of the Ward Melville Heritage Organization, which owns and operates the pond, said the flooding caused the pond’s dam to break. The rear of one nearby house was taken away, but everyone was safe, she said.

“It is a tremendous loss to our organization,” Ms. Rocchio said, adding that the pond was “nothing but a huge mud puddle now.”

The Suffolk County Police Department received dozens of calls overnight, including from drivers stranded in floodwaters and residents whose basements and first floors had been inundated, a police spokesman said. He added that the police had not received any reports of injuries.

The flooding also forced the closure of parts of some major highways and the suspension of some train service.

A portion of the Long Island Expressway, the major roadway connecting Long Island to New York City, was briefly closed for a two-mile stretch in both directions near the hamlet of Dix Hills early Monday, according to New York State authorities. New York State Route 25 was also closed in both directions near Dix Hills.

North of the city, the Bronx River Parkway was briefly closed for a two-mile stretch in both directions between the town of Scarsdale and the city of White Plains. Parts of the Harlem River Drive in Manhattan and the Major Deegan Expressway in the Bronx were blocked by flooding on Sunday, the police said.

Metro-North trains on the Danbury and Waterbury branches of the New Haven line were suspended through Monday afternoon after flooding and a mudslide in the area, the M.T.A. said.

Flash flood emergencies or flash flood warnings were declared in Connecticut on Sunday for parts of Fairfield, New Haven, Litchfield and Hartford Counties. In some places, the flooding was so severe that the police were unable to respond to calls.

Will Healey, a spokesman for the Connecticut Department of Energy and Environmental Protection, said in a statement that the agency had evacuated 43 campers and three department staff members from Kettletown State Park, more than 20 miles northwest of New Haven, on Sunday after a nearby bridge was washed out.

“There were no reported injuries, though one person was transported via ambulance for evaluation for a medical issue,” he said.

Among the most dramatic scenes was a flooded intersection in Southbury, where a man swam to a partially submerged car to rescue a driver, his prosthetic leg and his golden retriever.

The rescuer, Lucas Barber, said: “I pulled over, grabbed some rope that’s in the back of my car for emergencies, and threw my phone and wallet on the seat and ran out there.” Mr. Barber said he had checked the other nearby cars to ensure they were empty but had seen that Patrick Jennings, the man he rescued, was still inside his vehicle.

“He got me all the way out of the water, the dog comes swimming up and the rest is history,” Mr. Jennings said.