Fifteen-time major winner Woods, 50, was arrested after escaping unhurt from the accident in which he clipped a trailer he was attempting to overtake and rolled his Range Rover.
He was charged with driving under the influence, property damage and refusal to submit to a lawful test following last week's incident on Jupiter Island, Florida.
Woods was arrested and spent eight hours in custody on Friday before being bailed.
Martin County court documents showed Woods formally skipped an initial court appearance on Tuesday, but entered a written plea of not guilty via his lawyers and demanded a jury trial.
Bodycam footage of the aftermath of the crash released by the Martin County Sheriff's Office shows Woods making a phone call and can be heard saying "thank you so much" before being asked by an officer to stay "down here with us please".
Woods replied: "Yeah, I was just talking to the president."
It is not clear if he was referring to Donald Trump.
The US president told reporters following the crash: "I feel so badly. He's got some difficulty. He's a very close friend of mine, he's an amazing person, an amazing man."
In further bodycam footage, Woods described looking down at his phone before feeling a "boom" as he crashed his car.
The footage shows Woods, wearing sunglasses, on his knees being assessed for any injuries on a grass verge close to the accident site at a junction.
He described the moment he crashed by saying: "I look down at my phone and all of a sudden … boom."
When asked if he was comfortable, Woods replied: "Yeah, yeah." He was then told by the police officer he would be checked over by a doctor.
The officer then walked over to speak with the driver of the other vehicle, which was towing a trailer, with Woods's black Range Rover flipped on its side at the junction of a narrow side road.
The driver of the other vehicle, who was also unhurt, is reported to have said he was stationary in front of Woods's vehicle at the time of the collision.
More footage shows Woods undergoing various sobriety tests and two hydrocodone pills - a prescription used to treat severe pain - were found in his pocket during a search.
When asked by a police officer how much he had to drink today, Woods replied: "None."
When asked if he was taking any medication, he replied: "I take a few, yes." Woods added he had taken all his medication earlier that morning.
After his sobriety tests, Woods was handcuffed and told by the officer: "At this time I do believe that your normal faculties are impaired and you're under an unknown substance, so you are under arrest for a DUI."
It was the fourth occasion Woods has been involved in a motoring accident since 2009.
He has undergone numerous surgeries throughout his career, many to the leg and ankle, since suffering multiple injuries in a serious crash in 2021.
Prior to the incident, there had been speculation over whether Woods might play at the Masters – an event he has won five times – next week.
That will now not happen and the PGA of America said on Wednesday Woods had turned down the opportunity to captain the United States at the 2027 Ryder Cup after he announced he would step away from golf for a period to focus on his health and wellbeing.
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