NYPD sources tell TMZ they aren't investigating the independent presidential candidate. We also checked with the New York State Department of Environmental Conservation, and RFK Jr.'s in the clear there as well.

NYSDEC said they conducted a 2014 investigation into the Central Park bear cub's death, concluding the bear died from blunt-force trauma consistent with a high-speed collision. Due to a lack of evidence, they closed the probe later that year without issuing any citations.

Now, NYSDEC has the power to issue citations for the illegal disposal of a bear -- violators can be fined $250. Thing is ... there's a one-year statute of limitations on this offense, so RFK Jr. is way in the clear.

This comes a day after Kennedy owned up to the whole bear-in-the-park stunt that had locals scratching their heads for 10 years. RFK Jr. recounted the tale in an apparent attempt to get ahead of a story by The New Yorker ... which is now out and features a pic of RFK Jr. with the dead cub.

RFK posted a video on X ... saying he was driving during a hunting trip with his falcon when a woman in front of him struck and killed a bear. In the video, he's relaying the story to actor Roseanne Barr.

He grabbed the bear off the road because he says he didn’t want to let the meat go to waste ... but he got caught up with other stuff and never made it home to refrigerate the animal, so he just decided to dump it in Central Park.

RFK Jr. said, back then, there had been a bunch of pedestrians getting hit by cyclists in the park ... so he and his friends thought it would be funny to pin the bear's death on a bike rider.