Lucas Altman remembers it well: On an early October night in 2014, he had taken his two Labradors to Central Park when suddenly they became alert, their tails wagging with the thrill of the hunt as they towed him to a patch of shrubbery.

“It was dark, I was getting impatient and I didn’t bother to look,” he said.

A day later, he returned to find out that another resident had made a shocking discovery under the bushes: a dead bear cub, oddly placed under an old bike.

“It was so strange,” Mr. Altman, 52, remembered in an interview Monday. “I always thought it had to take somebody kooky to do that.”

This weekend, a most unexpected culprit stepped forward to admit the bear dumping: Robert F. Kennedy Jr.

Mr. Kennedy, the political scion whose independent presidential campaign has caused heartburn for both major parties, said he’d found the baby bear dead on a roadside and posed it as a prank. He revealed the decade-old stunt in a video he posted on social media Sunday, in expectation of a critical New Yorker profile published Monday that included the same anecdote.

Mr. Kennedy said he thought the staging would be “amusing,” though he seemed to understand that his sense of humor might not be for everyone.