In an e-mail, Smallcomb said no further details would be available pending the outcome of a coroner's investigation.
The bridge has been open for little more than a year, said Phil Frisbie, Jr., a spokesman for the California Department of Transportation.
At 255 feet, the bridge is a few feet taller than the Golden Gate Bridge, Frisbie added.
Concrete safety barriers were built on both sides of the Confusion Hill Bridge to make sure vehicles couldn't slide off the roadway, Frisbie said. A 54-inch tall metal fence was also installed to secure pedestrians and cyclists, he added.
"It's high enough to provide safety for pedestrians walking on the surface of the roadway or bicyclists riding on the highway," Frisbie said.
Jolly is the first person known to have fallen or jumped from the bridge, he said.
Doug Campbell, owner of a tourist attraction near the bridge, said Jolly didn't interact with anyone before he fell to his death.
Area residents, he said, have been buzzing about the circumstances surrounding Jolly's death.
The bridge has been the subject of concern for some locals who suspected that someone would one day leap from it, Campbell said.
"It was saddening, but everybody here locally was always thinking somebody was going to jump off it," he said.
Authorities have declined to comment on whether Jolly jumped or fell from the bridge, despite the roughly 4 1/2-foot pedestrian barrier.
Jolly had started his new position as superintendent of Round Valley Unified School District on July 1.
The district had has been operating under state and county oversight due to its troubled finances and student performance. It was a demanding job, but one that fitted Jolly's strengths, officials said.