Detectives in Florida released footage on Friday of the collision between a married couple and the tennis star, who was brought to tears at Wimbledon when she discussed the impact.
Mayor Paul Rogers said the surveillance footage shows Williams lawfully entered the intersection at a green light in her Toyota Sequoia near her home in Palm Beach Gardens at around 1pm on June 9.
But another car turned in front of Williams causing her to stop to avoid a collision before she legally continued, he added.
At this point a Hyundai being driven by Linda Barson, which was approaching a red light to Williams’ right, continued when the signal turned green.
Her car smashed head-on into the front-right of Williams’ vehicle, the officer said.
Mrs Barson, 68, and here 78-year-old husband Jerome were both injured and he died in hospital two weeks later on June 22.
Williams, 37, was not hurt and she was not charged with an offence. Investigators initially said she was at fault, but the video footage caused them to rescind that conclusion, and that no blame has yet been determined.
The Palm Beach Gardens Police Department said the investigation remains under way after inspecting the video evidence.
Mr Barson’s family launched a lawsuit against Williams, claiming she was “driving carelessly and recklessly”.
The five-time Wimbledon champion progressed to the fourth round of the tournament on Friday with a victory over Japan’s Naomi Osaka.
Williams, who is world number 11, overcame her opponent 7-6 (7/3) 6-4 on Court One.
Her sister Serena, the world number four, is not playing in the tournament this year as she is expecting her first child.