He put the bear’s body into the back of his car because he was going to skin the bear and store its meat at his house, he said.
But after a late dinner in New York City at the Peter Luger Steak House, he had to go straight to the airport and did not want to leave the bear in his vehicle.
“I had an old bike in my car that somebody asked me to get rid of. I said, ‘Let’s go put the bear in Central Park and we’ll make it look like he got hit by a bike,’” he said and then laughed, saying it would be “amusing” for whoever found it.
The Kennedy campaign did not immediately comment further on the incident.
In October 2014, the body of a black bear cub was found in the bushes of Central Park and police launched a criminal investigation into the death.
Foul play was suspected in the case, Reuters reported at the time, and state wildlife officials later concluded it was likely struck and killed by a vehicle.
Mr Kennedy said in the video that the New Yorker had asked him about the incident and was planning on doing a “big article” about him.
The New Yorker did not immediately respond to a request for comment from Reuters.
In a recent Reuters/Ipsos poll, Mr Kennedy was favoured by 8pc of voters. He has yet to qualify for the ballot in many states ahead of the Nov. 5 election.