Upon arrival at the family’s home, the team was shown into the kitchen. A child, who was three, the youngest of four home-schooled siblings, peeked from behind her mother’s legs, looking up shyly. She wore a baggy Minnie Mouse shirt and went to perch between her grandparents on a banquette, watching everyone take their seats around the dining table.

“Let’s start from the very beginning,” Dr. Tucker said after the paperwork had been signed by Misty, the child’s 28-year-old mother. “It all began with the puzzle piece?”

A few months earlier, mother and child had been looking at a wooden puzzle of the United States, with each state represented by a cartoon of a person or object. Misty’s daughter pointed excitedly at the jagged piece representing Illinois, which had an abstract illustration of Abraham Lincoln.

“That’s Pom,” her daughter exclaimed. “He doesn’t have his hat on.”

This was indeed a drawing of Abraham Lincoln without his hat, but more important, there was no name under the image indicating who he was. Following weeks of endless talk about “Pom” bleeding out after being hurt and being carried to a too-small bed — which the family had started to think could be related to Lincoln’s assassination — they began to consider that their daughter had been present for the historical moment. This was despite the family having no prior belief in reincarnation, nor any particular interest in Lincoln.

On the drive to Amherst, Dr. Tucker confessed his hesitation in taking on this particular case — or any case connected to a famous individual. “If you say your child was Babe Ruth, for example, there would be lots of information online,” he said. “When we get those cases, usually it’s that the parents are into it. Still, it’s all a little strange to be coming out of a three-year-old’s mouth. Now if she had said her daughter was Lincoln, I probably wouldn’t have made the trip.”

Lately, Dr. Tucker has been giving the children picture tests. “Where we think we know the person they’re talking about, we’ll show them a picture from that life, and then show them another picture — a dummy picture — from somewhere else, to see if they can pick out the right one,” he said. “You have to have a few pictures for it to mean anything. I had one where the kid remembered dying in Vietnam. I showed him eight pairs of pictures and a couple of them he didn’t make any choice on, but the others he was six out of six. So, you know, that makes you think. But this girl is so young, that I don’t think we can do that.”