The video, from a dashboard camera in the vehicle of Jupiter, Florida, police officers, shows Woods unable to tie his shoe and wobbling as he tries to walk along a straight line in a field sobriety test.
Woods has blamed the DUI arrest near his home on an adverse reaction to prescription medication.
The police report on the incident, made public on Tuesday, said Woods was "cooperative" and "confused" when found by police, with "extremely slow and slurred speech."
Woods is unable to follow a light with his eyes when asked to do so. When officers ask if he understands instructions to recite the alphabet, he says he was asked "not to sing the national anthem backwards."
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At one point in the sobriety tests Woods asks, "What are we doing?"
The 14-time major champion was taken into custody at 2:49 am Monday, booked into jail at 7:18 am and released on his own recognizance at 10:50 am.
He was discovered by police asleep in his car in the right lane of a road, his right turn indicator blinking and the motor running.
Woods told police he was taking several prescriptions, including two painkillers. His breathalyzer test showed no sign of alcohol.
"I understand the severity of what I did, and I take full responsibility for my actions," Woods said in his statement on the incident.
"I want the public to know that alcohol was not involved. What happened was an unexpected reaction to prescribed medications. I didn't realize the mix of medications had affected me so strongly."
Woods announced last week he had undergone a fourth back surgery in April that will keep him off the course for the rest of the 2017 season, and he is unlikely to engage in strenuous physical activity for months.
He attempted a comeback after more than a year away from the game late in 2016 but played in just three tournaments.
After coming back at an unofficial event in December, he missed the cut in January at the Farmers Insurance Open and withdrew after one round of a tournament in Dubai in February.
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