Photo: Eric Thayer for The New York Times; Video: By THE ASSOCIATED PRESS

Hillary and Bill Clinton felt at home. The former first couple, hoping to return to the White House, made their way to Douglas A. Grafflin Elementary School in Chappaqua early Tuesday to say hello to their neighbors and cast their votes.

As the crush of reporters following Mrs. Clinton became particularly intense, she said, “Guys, it’s supposed to be a private ballot” as the media scrum circled around her.

But Mrs. Clinton seemed at ease around the neighbors who have known the Clintons since they moved to Chappaqua after leaving the White House.

After voting, the Clintons worked the crowd that had assembled outside. Not a single Bernie Sanders sign could be found here in Clinton Country, and they fellow Chappaqua residents for about 20 minutes.

People chanted “Hillary! Hillary!” and there was an energetic contingent of children holding handmade “Kids for Hillary!” signs. They started a chant “When I say Madam, you say president!”

Mrs. Clinton, aware of state laws that prohibit any political activity within 100 feet from a polling location, did not comment on the state of the race, but she did urge people to vote.

“I love New York and this has been a joy during the last two weeks to be here, all over the state,” she told reporters. “I hope everybody gets out to vote. I’ve had a great time going around the city in the last couple of days, meeting new people, seeing old people and I just urge everybody to go vote.”

After voting, Mrs. Clinton made a quick dash to Washington, D.C. to deliver a speech and Mr. Clinton headed to a phone banking office in White Plains, N.Y. to greet volunteers, many of whom shared stories of either working for the Clintons or previously meeting them.

“I remember it well,” Mr. Clinton would tell people, and in most cases he did, in almost every detail.

“I’ve been to your house!” an elderly woman said. “When Hillary ran the first time, she showed us around your house.”

Mr. Clinton tried not to get ahead of himself about Tuesday’s results.

“I just look at the next election. All I know is tomorrow morning I’m going to Pennsylvania and I think I end up in Connecticut and I’ve got to go back to Rhode Island — and every place north of here is a bigger challenge,” Mr. Clinton said, and he listed Kentucky, West Virginia, Oregon and Puerto Rico “where I think she’ll do great.”

“My theory is stay in the fight you’re in, drown everything else out,” Mr. Clinton said in an interview.

As for what will happen on the Republican side and whether there will be a brokered convention, the former president played coy about the GOP race. “I don’t understand their rules enough to know,” Mr. Clinton said. “I’ve been so obsessed with ours.”

Afterwards, Mr. Clinton wandered across the street to shake hands with mostly immigrant pedestrians who crowded out of bodegas to get a glimpse of the former president.

“That woman came from Medellin, Colombia, with Bangladeshi” markings on her hands, he said. “That’s New York.”

He relayed his conversation with the woman to a reporter: “I said your city is free now and she said ‘I know and we love you for it.’”

Asked whether Mrs. Clinton could use the diversity of New York to portray Donald J. Trump as intolerant, Mr. Clinton said, “If she wins the nomination, she’ll be able to do this.” He added: “That’s what we’ve got to do again. We’ve got to make people understand that all these young people from all over the world are a huge asset to us.”