On Monday, the Center for Biological Diversity Action Fund, a nonprofit group, wrote a letter to directors of the National Oceanic and Atmospheric Administration asking them to investigate Kennedy for his alleged actions, which his daughter, Kick Kennedy, recounted to Town & Country in a 2012 interview. The story resurfaced this week amid tabloid reports about Kick Kennedy's dating life.
According to the Town & Country piece, "Word got out that a dead whale had washed up on Squaw Island in Hyannis Port, [Massachusetts]."
"Bobby -- who likes to study animal skulls and skeletons -- ran down to the beach with a chainsaw, cut off the whale's head, and then bungee-corded it to the roof of the family minivan for the five-hour haul back to Mount Kisco, New York," according to the article.
A spokeswoman for Kennedy did not respond to a request for comment.
Kick Kennedy told the outlet, "Every time we accelerated on the highway, whale juice would pour into the windows of the car, and it was the rankest thing on the planet. We all had plastic bags over our heads with mouth holes cut out, and people on the highway were giving us the finger, but that was just normal day-to-day stuff for us."
Robert F. Kennedy Jr. last week suspended his independent presidential campaign and endorsed Republican Donald Trump. Trump's campaign announced later that Kennedy would join his presidential transition team.
In the letter to the NOAA, Brett Hartl, national political director for the Center for Biological Diversity Action Fund, argued that Kennedy, a former environmental lawyer, violated the Marine Mammal Protection Act and possibly the Endangered Species Act.
"We hope that the NOAA Office of Law Enforcement, at a minimum, is able to ensure that Mr. Kennedy surrenders any and all illegally obtained wildlife that he continues to possess, including the whale skull he took from the Massachusetts beach in 1994," Hartl wrote, according to a copy of the letter he provided to ABC News.
"Given Mr. Kennedy's reckless disregard for the two most important marine conservation laws in the United States, we ask that NOAA consider all appropriate civil and criminal penalties as well."
Representatives for the NOAA did not respond to an emailed question about whether the agency had decided to investigate Kennedy.
The resurfaced whale anecdote is the second story regarding Kennedy's handling of wild animals that has drawn attention and scrutiny this summer.
Earlier this month, he told Roseanne Barr that in 2014 he jokingly planted a dead bear cub in Central Park after picking up the cub from the side of the road and putting it in the back of his vehicle.