Leffler was taken to Crozer-Chester Medical Center and pronounced dead at 9:02 p.m., Jones said. Leffler's body has since been taken to the Delaware County Medical Examiner's Office.
The fatal-accident unit of the New Jersey state police is investigating the crash.
Officials postponed the remainder of Wednesday's race. Bridgeport's next event is scheduled for Saturday, but it is unclear when the track will reopen. The owners and managers did not return phone calls and e-mails seeking comment.
The accident occurred during the second lap of the first heat, said Joe Grandinetti, regional director for the Tri-State Racing Series, which entered teams in Wednesday's race.
He said conditions at the track - which opened in 1972 - were fine. "It was a tragic accident. I've been racing over 50 years. I've seen just about everything that can happen ... from flaggers being killed to drivers," Grandinetti said.
"It happens. No matter how much safety you try to put in, sometimes it just happens. We do our best. This was something that just happened."
A sprint car is a high-powered open-wheel vehicle originally designed in the late 1930s and early 1940s. There is no clutch. The driver must put the vehicle in gear and a push-truck fires the car up, Grandinetti said. Once a driver has completed a race, the driver must pull it out of gear with a cable that stretches from the cockpit to the rear of the car, he said.
After a successful stint on a lower-profile circuit, Leffler joined the NASCAR Nationwide Series in 2000, according to his website. The Associated Press said Leffler made 423 career starts in NASCAR's three series, including two in Nationwide and one Truck Series event.
Leffler finished 17th in the 2000 Indianapolis 500. He won three consecutive U.S. Auto Club midget championships from 1997to 1999 before making the jump to NASCAR, the AP reported.
He did not race regularly on the Sprint Cup level, but in March announced he would return to his "grassroots in the open-wheel world." He competed June 9 at Pocono Raceway in Long Pond, Pa., and finished last.
Grandinetti, who described himself as an acquaintance of Leffler's who has been racing at Bridgeport for 14 years, said drivers, crew workers, and fans were aware of the risks associated with racing.
He recalled an experience he said suggested the random nature of fatal accidents.
"Just to show you how things work: My first year, I was leading the race. There was a guy running in second. He took his eyes off the track for a split-second to see where my car was, caught the inside guard rail, hit the fence 20 feet more into the corner than where Jason hit it, head-on, well over 100 m.p.h.," he said.
"It hit so far that it broke the engine in half. We all thought he was dead. He gets out of the car, walks to the ambulance." The only problem was a cut on a hand.
Not all drivers have been so lucky. Two were killed last month on dirt tracks in Indiana and Nevada, the AP reported, and two others were killed in March when a car crashed on a pit row in California.
On Thursday, NASCAR posted a video tribute to Leffler on its website, showcasing his career highlights.
"NASCAR extends its thoughts, prayers, and deepest sympathies to the family of Jason Leffler," it said in a statement. "For more than a decade, Jason was a fierce competitor in our sport, and he will be missed."
Fellow NASCAR drivers expressed their condolences on social media; many mentioned Leffler's 5-year-old son, Charlie Dean.
"Such sad news, we lost a great one last night. My thoughts and prayers go out to @JasonLeffler's family. #LEFTurn," five-time Sprint Cup Series champion Jimmie Johnson wrote on Twitter, referring to Leffler's nickname, which he would write above his driver's-side window.
Tweeted 2004 champion Kurt Busch: "Just woke up & saw the news about @JasonLeffler - can't believe it. #prayers for his family 4 this devastating loss. #rip Jason."
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