Palm Beach Gardens police in Florida have released a report saying the tennis star was at fault in the crash on 9 June.
Jerome Barson, a 79-year-old who was a passenger in his wife’s car, was injured and died two weeks later.
The police report says witnesses have claimed Williams ran a red light at a junction and went into the path of the vehicle driven by Mr Barson’s wife.
Williams, who is preparing to compete at Wimbledon next week, was driving her 2010 Toyota Sequoia SUV at the time.
The police department’s Major Paul Rogers said the crash remains under investigation and Williams has not been cited or charged.
