Sheriff Budensiek told reporters at a news conference that the crash happened after Woods allegedly attempted to overtake a pressure cleaner truck at “a high rate of speed”.
DUI investigators came to the scene and “Mr Woods did exemplify signs of impairment”, the sheriff said.
“They did several tests on him,” Budensiek told reporters. “He did explain the injuries and surgeries that he’s had and we did take that into account, but they did some in-depth roadside tests.”
He was placed under arrest after the incident, which took place on Beach Road in Jupiter Island just before 14:00 local time on Friday (about 19:00 GMT).
The sheriff explained that investigators at the scene and jail were “really not suspicious of alcohol being involved” and Woods ultimately passed a breathalyser test with “triple zeros”. But, he added, Woods then refused a urine test.
Budensiek also said Woods had been “co-operative but was trying not to incriminate himself”.
“He has a right to refuse that test,” added the sheriff. “There is a statute which he will be charged with for refusing to take that test, but we will never get definitive results as to what he was impaired on at the time of the crash.”
US president Donald Trump was asked about the crash on Friday, saying: “I feel so badly. [Woods has] got some difficulty. There was an accident. That’s all I know.
“He’s a very close friend of mine, he’s an amazing person, an amazing man.”
Sheriff Budensiek said Woods would remain in jail for eight hours then be released on bond. The charges are misdemeanours, not felonies.
The BBC has contacted the golfer’s representatives for comment.