Sheriff Philip C. Povero told reporters that the Ontario County medical examiner finished an autopsy on the 20-year-old driver on Monday.
Povero also said investigators were reviewing a second video of the incident in which Stewart's car struck Ward as the young driver stood on the dirt track after a spin out. Ward died of his injuries before an ambulance arrived at a hospital.
The sheriff said the investigation was progressing well, but gave no timeline as to when it would wrap up.
He reiterated that there was no evidence at this point that a crime has been committed.
Investigators spoke to Stewart's representatives on Monday, the sheriff said. Stewart was interviewed after the incident, authorities have said.
On Saturday night, Ward's sprint car hit the outside wall during lap 14 of a 25-lap race put on by the Empire Super Sprints series at the Canandaigua Motorsports Park in upstate New York.
A video of the incident shows two cars coming out of a turn with Stewart's No. 14 car sliding up the track toward Ward's No. 13 car. The two cars get close and appear to make contact before Ward's car hits the wall and spins out. Another car narrowly avoids hitting the 13 car as its sits on the track facing the wrong direction.
Ward gets out of his crashed car and walks determinedly on the track toward the race cars, which had slowed for a yellow flag. Ward points a finger and appears to be yelling. One car swerves to avoid Ward on the half-mile dirt track.
Stewart's car passes close to Ward, and it appears that its right rear tire hits him.
The second video was taken from a different angle, the sheriff said without elaborating.
Ward's funeral will be held Thursday, according to an update on the Empire Super Sprints website.
"The entire Ward family sends their sincere thanks to all that has send their heartfelt notes, calls, texts, anything that has been sent their way," the post says, adding the family is "very proud of Kevin."
Stewart express sadness
"There aren't words to describe the sadness I feel about the accident that took the life of Kevin Ward Jr.," Stewart said Sunday, according to a written statement tweeted by NASCAR. "It's a very emotional time for all involved. ... My thoughts and prayers are with his family, friends and everyone affected by this tragedy."
Stewart decided not to take part in Sunday's NASCAR event at Watkins Glen, New York. Whether he competes in this weekend's event is still undecided.
"The decision to compete in this weekend's NASCAR Sprint Cup Series event at Michigan will be Tony's, and he will have as much time as he needs to make that decision. It is still an emotional time for all involved, Tony included. He is grieving, and grief doesn't have a timetable," spokesman Mike Arning said.
Ward began racing at 4
Ward, from Port Leyden, New York, was in his fifth season in the Empire Super Sprints series. He began racing when he was 4, running go-kart events.
A competitor who runs the car that swerved around Ward expressed sympathy.
"Our deepest condolences go to the entire Ward Family. We are one huge ESS family, you will be truly missed bud! #RIP13," Hebing Racing tweeted.
Stewart is a three-time champion in NASCAR's top division and won a sprint car championship in 1995.
He also owns a dirt race track in New Weston, Ohio, and has frequently raced sprint cars, even during the NASCAR season. He broke a leg last year in a sprint car crash that ended his racing season. He has raced the full NASCAR season this year but only returned to sprint cars in July.
CNN's Dave Close, Chris Welch, Jason Durand, Stephanie Gallman and Joe Sutton contributed to this report.