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Appealing to members of the public to help catch the "heartless thug," the UK branch of People for the Ethical Treatment of Animals (PETA) urged anyone with details about the "infamous" case to contact the Grand Canyon's chief ranger.
In the video, a shirtless man is seen apparently feeding the squirrel before booting it off the edge of a cliff and into the crimson-hued canyon. It has since been removed by YouTube.
Park rangers have been investigating since they were alerted to the existence of the video earlier this week, and they believe it was filmed within Grand Canyon National Park.
Few other details are clear, said park spokeswoman Kirby-Lynn Shedlowski, including when and exactly where the recording might have been made.
If caught, the person responsible could face a charge of wildlife harassment, which carries a penalty of up to six months in jail and a $5,000 fine, Shedlowski said.