BRANFORD, Conn. — Ted Kennedy Jr. FES ’91 made a pledge to vendors on a recent weekend at the Trinity Church Fair on the town green: “Next time, I’ll bring my appetite.”

What went unsaid was that he expected their votes in return.

Kennedy is running for the Connecticut State Senate in the 12th district, which comprises six towns, including this shoreline community just eight miles outside of New Haven. His visit to the annual fair, hosted by the Trinity Episcopal Church, was the first stop in a day’s tour through the three shoreline towns in the district: Branford, Madison and Guilford.

The candidate wanted to talk about the future — about “next time” — and about what lies ahead for Connecticut.

But the people who greeted him wanted to talk about the past — his family’s and his own. Across folding tables piled high with second-hand wares, from needlework to vacuum cleaners, Kennedy heard just as much about his own life as about the lives of Connecticut voters.

Wendy Cowles, president of the Branford Food Pantry, told the candidate that she was a student nurse in 1964 at Cooley Dickinson Hospital in Northampton, Mass., when his father — the late U.S. Senator Ted Kennedy — was involved in an airplane crash en route from Washington to Massachusetts that sent him to the hospital.

“You were upset you couldn’t jump on your father’s back,” she reminded Kennedy, who nodded, his sharp, blue eyes coming to rest on Cowles as he registered the connection. Kennedy was roughly two years old at the time.

Now, as the candidate turns 53, his broad shoulders and square features resemble the late senator. His sonorous voice echoes his father’s. Having lost his right leg to pediatric bone cancer when he was 12, Kennedy walks slowly and methodically, with a slight limp.

A resident of East Haven, Cowles will not be able to vote for Kennedy in the upcoming election, in which he is facing Republican businessman Bruce Wilson Jr. for the seat Edward Meyer ’57 LAW ’61 is relinquishing at the end of the year.

Based on what she knows of the candidate’s past, though, she is already charting his future.

“I hope he runs for president,” Cowles said, extolling the Kennedy family as honest and civic-minded. “I think the whole bunch of them, from his uncle to his father, wanted to help people.”

Kennedy, a health care lawyer and resident of Branford, has spent nearly three decades seeking independence from the family business. He created physical distance by leaving Massachusetts, the state at the heart of his family’s political fortunes. Kennedy attended college at Wesleyan in Middletown, Conn., continuing his studies in New Haven at the Yale School of Forestry & Environmental Studies.

Under professors such as John Wargo GRD ’84, who studies environmental health and politics, Kennedy focused on the public health aspects of environmental contamination. He looked in particular at toxic substances in everyday products, he said, pointing to his bottle of Coke Zero on the table in front of him in a cafe on the Guilford Green.

“Particularly in this district, environmental protection and public health are important issues,” he said. With a population of roughly 61,000, the district is adjacent to the Long Island Sound. “There’s an environmental component to every public policy decision.”

Of course, he said, jobs and the economy come first. Before he settled in Branford, he observed the importance of these issues in New Haven, outside his classwork at the forestry school.

Kennedy lived on Academy Street in Wooster Square and met his wife-to-be, Katherine Anne “Kiki” Gershman, through a mutual friend and mentor, Robert Thompson ’55 GRD ’65, a longtime master of Timothy Dwight College. Gershman, now an assistant clinic professor of psychiatry at the Yale School of Medicine, was doing her residency in New Haven at the time, serving as the psychiatric liaison to Timothy Dwight.

After getting a law degree at the University of Connecticut, Kennedy worked in New Haven at the firm Wiggin & Dana, litigating disability-related cases. He later founded a health care and financial services firm called Marwood Group, which is headquartered in New York.

About 20 years ago, he settled in Branford. Around the same time, he had his first child, a daughter who is now a student at Wesleyan. A son came four years later.

Throughout, questions lingered about possible political ambitions. When former U.S. Sen. John Kerry ’66 became the presumptive replacement for Hillary Clinton LAW ’73 as Secretary of State, Kennedy’s name was mentioned as a possible successor, scarcely three years after his father had died while holding the seat.

Instead of returning to Massachusetts and positioning himself as the presumptive heir to his father’s legacy, though, Kennedy stayed in Connecticut. Now, rather than making a play in a statewide race, he is spending these weeks at town fairs and farms, shaking hands and introducing himself to people over pancakes.

“I’d always thought about running, you know, coming from a political family,” Kennedy said during the stop in Guilford. “But I really wanted to focus on raising my children, and now they’re 16 and 20 years old.”

As for his decision to run in Connecticut and not Massachusetts, the rationale is simple, he said: “Well that’s where I live. I’ve been in Connecticut for 30 years.” He said he has enjoyed being outside the “power centers of Boston or New York or Washington, D.C.,” wanting to “develop my own interests and expertise.”

At the same time, Kennedy does not shy away from invoking his family for rhetorical flourish. Addressing campaign volunteers at headquarters in Madison, where Democrat Alex Taubes LAW ’15 is running to unseat the Republican incumbent, Kennedy hailed face-to-face voter contact as a vital campaign strategy.

“This is a tradition. You’re part of a tradition here. My uncle — he knocked on doors,” he said, as if welcoming campaign workers into a family ritual, one reaching all the way to the White House.

That gesture has inspired a gaggle of interns to devote time to Kennedy’s campaign. Jack Lazor, a senior at Daniel Hand High School, said a career in politics is already in the back of his mind.

Thomas Banisch, chairman of Madison’s Republican Town Committee, said Kennedy’s name has slanted media coverage of the race. Because “everything we’ve seen so far is about Ted Kennedy, nothing about Bruce Wilson,” he said, “I don’t think we’re going to get fair treatment.” Wilson did not return multiple requests for comment.

Kennedy’s name notwithstanding, the race is going to be close, according to campaign manager John Murphy, an assistant business manager for an electrical workers’ union. “My job is to be paranoid,” he said. Like many areas on the shoreline, the district has an outsized proportion of unaffiliated voters, putting Democrats and Republicans both in the minority.

Murphy said he does not envision Kennedy making a play for higher office, as much as supporters wish he would.

“People say, ‘Why would you settle?’” Murphy said, scaling back perceptions of the candidate’s ambitions. “He really doesn’t want to go to D.C.”

Still, Cowles and other supporters — including a vendor at the Dudley Farm who praised Kennedy’s candidacy as “step number one” — are holding their breath.