In body camera video of Mr Damon's arrest on charges of driving under the influence, the ex-New York Yankee and Boston Red Sox outfielder is seen slurring his words as he explains his support for Blue Lives Matter.
"Hey bro, I'm a good f***ing guy, and I know people are trying to target me because I'm a Trump supporter," Mr Damon said to the officer.
When the officer responds that support for the ex-president did not have anything to do with the traffic stop, Mr Damon maintained that, "yeah, it does".
"That's neither here nor there right now. That's not why I'm stopping you," the officer replied.
A former contestant on Celebrity Apprentice, Mr Damon endorsed Mr Trump during the 2016 presidential campaign, saying that he wasn't a racist and just wanted people to enter the country legally.
"I'm a Trump fan ever since I met him seven or eight years ago. Everything he does, he does first-class — his hotels, his businesses, his golf courses. The issues all the other politicians failed to discuss, (Trump) is bringing us up to speed," he told The New York Daily News in 2016.
The two-hour video, released on Tuesday as part of a public record request from local WKMG News 6, showed the 19 February arrest in Orlando, Florida, during which Mr Damon allegedly had a blood-alcohol level nearly four times the state limit of 0.08.
During the stop, Mr Damon can be heard saying he's "good bro" and that he was just trying to get home.
"Believe me, I am Blue Lives Matter ... What are you doing right now? We are all for cops. Guys, we are all for cops," he said.
The two-time All-Star and World Series champion, with the Red Sox in 2004 and Yankees in 2009, has entered a plea of not guilty to the DUI charge while his wife, Michelle Mangan-Damon, was charged with battery on a law enforcement officer and resisting an officer, according to WKMG News 6.
Speaking in February after being released from Orange County jail on bond, Mr Damon said he's "always accountable" for his actions.
“I will be honest with you and always be accountable and like I said I would never put myself, my loved ones or anybody in harm’s way getting behind the wheel of a vehicle. So, I apologise and hopefully, I can answer more questions later on,” he said.
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