“I’m out in nature. I’m just doing the complete opposite of what I thought I loved,” Ms. Rosati said. “I’m not going back to the city.”

After renting in Wilton, the 55-year-old signed a contract for a four-bedroom home on 3 acres in the town of Easton.

Connecticut’s suburbs have long had a seesaw relationship with the nation’s largest city, benefiting from New York’s problems, then losing out when the city rebounded.

The last time Connecticut reaped significant rewards was the mid- to late-20th century, when New York City suffered from a surging murder rate and fiscal troubles. Connecticut beckoned to businesses and employees with safe towns, good schools and—until the early 1990s—no personal income tax.

Many major New York companies decamped to Fairfield County in the late 1960s and 1970s, including industrial conglomerate General Electric Co., energy firm Conoco Inc., smokeless-tobacco maker U.S. Tobacco and Chesebrough-Pond’s, the maker of Vaseline before a later acquisition.

Connecticut added 196,700 jobs during the 1980s, a 14% jump, many in the insurance and finance sectors. In 1986, pharmaceutical company Bristol-Myers opened a sprawling new research lab in Wallingford, Conn., that would eventually employ 1,300 people pursuing treatments for HIV, heart disease and cancer.

The economic winds began shifting in the early 1990s, when a tough recession hit the state hard.

Political leaders “believed their suburban economic strategy, which had been very successful in the ’70s and ’80s, would always carry the state through,” said Joseph J. McGee, who was commissioner of the state’s economic-development agency in the early 1990s. “And when that strategy changed abruptly because people wanted to live more in the cities, they were not prepared.”

Connecticut found itself sandwiched between two major metropolitan areas, but without a big city of its own. To the northeast, Boston has grown 21% since 1990, buoyed by its position as a life-science boomtown. General Electric, after more than four decades in suburban Fairfield, Conn., moved its headquarters to Boston in 2016.

Two years later, Wallingford lost its largest taxpayer when Bristol-Myers Squibb Co. shut down its lab, as part of a larger move that included shifting cancer research to an expensive neighborhood filled with biotechnology firms in Cambridge, Mass.

The state’s leaders aren’t sure if New York transplants are there to stay or just riding out the storm, but they want to keep them, said David Lehman, Gov. Ned Lamont’s top economic-development official.

“We are going to market ourselves more to those individuals as opposed to marketing ourselves to the company,” he said, regarding efforts to lure businesses. Commercial real-estate experts believe the trend of people steering clear of crowded offices and working from home could long outlast the pandemic.

If this new craving for suburban living leads to just a 5% increase to the state’s labor force, including people working from home, that would be a huge boost in tax revenue, Mr. Lehman said.

The newfound demand for Connecticut’s suburbs has potential for the entire state, but particularly for Fairfield County, which still puts residents within commuting reach of New York, Mr. Lehman said. The state isn’t giving up trying to revitalize its own cities, which will remain important in the post-pandemic world, he said.

The state’s poor economic performance after the last recession will continue to dog Connecticut as it tries to rebound from the current crisis, said Don Klepper-Smith, chief economist at consulting firm DataCore Partners.

“Connecticut has dug itself into a hole here,” he said. “I think the state economy is going to underperform for the next several years.”

A long-running challenge for Connecticut is its reputation for high taxes. The Tax Foundation, a conservative-leaning think tank, ranks Connecticut 47th on its state business tax climate index.

The tax argument holds less sway for New Yorkers. Connecticut’s top income-tax rate is lower than New York state’s, plus New York City also collects an additional income tax.

New Yorker Stacie Black, 38, said lower property taxes on the Connecticut side of the border are a draw in her continuing search for a house there and in New York’s Westchester County. She and her fiancé recently listed their home on Manhattan’s Upper East Side.

“The homes that we can afford in Connecticut are probably $100,000 more than the homes we can afford in Westchester just because of the taxes,” she said.

Ms. Black, who sells event space in the hospitality industry, has been weighing Connecticut’s relative affordability against longer commute times. She isn’t interested in long, daily trips to the city, but is more willing if she sticks at least partially to a work-from-home schedule. “I could manage it for two days a week,” she said.

Commercial real-estate experts say New York City-based businesses have been scouting suburban offices, including in Connecticut, as they contemplate bringing at least some workers back to cubicles. Citigroup Inc. confirmed it is contemplating leasing office space in Connecticut, among other areas in the greater New York region.

Darin Buelow, global location strategy leader at Deloitte Consulting, said he has heard more broadly of financial firms “that are looking at space in suburban markets, including Connecticut, or they’re going to.” Suburban offices may prove easier to access in a protracted pandemic than city high-rises reached by congested trains and elevators, he said.

“I think companies are starting to hedge their bets a bit and look around,” he said.

Before the pandemic hit, Felix Charney and his partners Crestline Investors Inc. were in the midst of a commercial and residential redevelopment of the nearly empty former headquarters of Union Carbide Corp., which fled New York City for the futuristic-looking Danbury office in the early 1980s.