Over dinner at the Belle Haven Club in Greenwich, a member of United Technologies Corporation’s board of directors, Harold “Terry” McGraw, was talking about gubernatorial politics when, according to a fellow diner, the director asserted that UTC would exit Connecticut if Democrat Ned Lamont is elected governor.

“Terry McGraw said if Lamont was elected, they were going to move from Connecticut,” said Walter Raquet, the author of “Government is Killing the Economy” and one of about 40 guests at a dinner earlier this month organized by the conservative think tank, the Hoover Institution. “He didn’t really elaborate on it.”

McGraw declined in a telephone interview to confirm or deny making the comment, instead downplaying whatever was said over dinner as political chatter with table mates, not a pronouncement of intent by UTC, the corporate parent of Pratt & Whitney, Otis Elevator Company, and other concerns.

“It would be inappropriate of me to make any comment on behalf of the company,” said McGraw, the former chairman of McGraw Hill. “That definitely should come from the company.” UTC declined to comment.

The remark attributed to McGraw would be a striking departure for a corporate Connecticut that generally steers clear of trying to directly influence gubernatorial elections, even in an era when corporations are legally permitted to make unlimited independent expenditures in support of or in opposition to individual candidates.

Lamont, Republican Bob Stefanowski, and Oz Griebel, a petitioning candidate who once ran Greater Hartford’s largest business association, the MetroHartford Alliance, all have been trying to win the hearts and minds of a business elite that is increasingly willing to engage candidates in conversation, while remaining coy on the matter of endorsements.

“At least in my recollection, that’s always been the case,” said Joseph Brennan, the president of the Connecticut Business and Industries Association.

There are exceptions. A political action group affiliated with the Connecticut Realtors endorsed Stefanowski, as did the National Federation of Independent Businesses. The latter group routinely endorses candidates.

Brennan said while business executives generally refrain from endorsements, they are ready to work more directly with the next governor, given the state’s fiscal and economic challenges and the business backgrounds of Lamont, Stefanowski and Griebel.

“There is a high level of interest in the business community and corporate community to really engage with the next governor in a way I’ve never seen before,” Brennan said.

Last week, Lamont and Stefanowski met with the senior leadership of Stanley Black & Decker, which has invited all five gubernatorial candidates to meetings. Griebel is scheduled to visit Monday. Also on the ballot are Rod Hanscomb, a Libertarian, and Mark Stewart Greenstein, a registered Democrat running as a pro-business independent.

“The company has been focused on the broad issues around fiscal stability and economic growth,” said Shannon Lapierre, the company’s vice president of communications.

On Friday, Griebel had a similar session at Boehringer-Ingleheim, a global pharmaceutical company with a sprawling office campus in Ridgefield and Danbury. The conversation turned on the cost of doing business, workforce development and retention, and transportation issues, Griebel said.

Candidates make their case and answer questions without hope of an endorsement, he said.

“You’re not going to get a commitment,” said Griebel, who took a leave from the MetroHartford Alliance to run for the Republican gubernatorial nomination in 2010. Griebel, 69, retired last year to run for governor as a petitioning candidate.

Stefanowski, 56, of Madison was between corporate jobs in early 2017 when he attended a dinner in New York for Gov. Rick Scott of Florida. Stefanowski said he was seated next to John Fund, a conservative writer who suggested that the businessman consider running for governor, saying Connecticut was in desperate need of a business-like approach to government.

Stefanowski had recently stepped down as chief executive officer of DFC Global, a Pennsylvania-based owner of payday lenders, pawn shops and other sub-prime consumer lenders. He previously was an executive at UBS Investment Bank, GE and 3i, a British investment company.

Lamont, 64, of Greenwich is the founder and owner of Lamont Digital, a holding company that sold its primary business in 2015, a small cable television company called Campus Televideo. He is running as candidate who could bring business leaders to the table to help improve Connecticut’s business climate.

Lamont, Stefanowski and Griebel all say they understand the needs of business, promising to reduce regulations and lower business taxes, as the state’s fiscal conditions allow.

Stefanowski has been most aggressive, saying he believes he could eliminate the state income tax over eight years and reduce or even eliminate the corporation tax, while raising no other taxes. Lamont and Griebel say Stefanowski at best is engaging in fantasy, or at worst hinting at a willingness to engage in a destabilizing fight over slashing services and taxes.

Stefanowski said neither of his opponents have the vision or ambition to make major change in Connecticut, and calls Lamont a late-comer to the belief that Connecticut needs lower taxes to grow its economy.

None of the candidates have provided a detailed approach to closing the $2 billion budget shortfall the next governor will likely face in January, the start of the new term.

Lamont’s campaign recently announced the names of a dozen chief executives or other top corporate leaders who have agreed to serve on a business advisory council should he be elected, a way for the executives to offer a measure of support that falls short of an endorsement.

They include Indra Nooyi of PepsiCo, Cindi Bigelow of Bigelow, Adam Norwitt, of Amphenol, Tony James of Blackstone Group, Alan Schnitzer of Travelers, Elliot Joseph of Hartford HealthCare, and Roxanne Coady of RJ Julia Books.

Lamont said he has conducted roundtable talks with 60 chief executives.

Absent from the list is Gregory Hayes, the chairman and chief executive officer of UTC, who has been more encouraging about doing business in Connecticut since famously complaining to Wall Street analysts during the administration of Gov. M. Jodi Rell about the high cost of doing business in the state.

“I think I met with virtually every CEO in the state except for Greg Hayes. We had others reach out,” Lamont said, adding that he still would like to meet with Hayes.

Lamont, who said he heard about McGraw’s comments at the Belle Haven Club, dismissed them.

Stefanowski said it was interesting that Hayes took a meeting with him, but not Lamont.

“I met with Greg Hayes, and we talked about what we can do to stimulate Connecticut’s economy, and he liked my plan about lowering taxes and creating jobs.”

Under Hayes, UTC has deepened its commitment to Connecticut, renovating and expanding its research center on the Pratt & Whitney campus in East Hartford. The state approved a $400 million tax-relief package for UTC in 2014, drawing a pledge from UTC for $500 million in investments on four major capital projects, including $60 million for the 185,000-square-foot research center. It also included the construction of a new, 425,000-square-foot world headquarters and engineering facility for subsidiary Pratt & Whitney in East Hartford.

Gov. Dannel P. Malloy helped open the facility a year ago, when UTC announced two more investments, a $75-million additive manufacturing research center and a $40-million engine compressor testing and research facility.

“This is a great example of why Connecticut is a great place to do business,” Hayes said then. “A tribute to why we think Connecticut is the right place to be for the future.”