A DuPage State's Attorney's Office spokesperson tells TMZ Sports ... it all started after law enforcement responded to a report of a battery at a motel on July 27 in Oakbrook Terrace, IL.

The spokesperson says Kennedy was accused of violently attacking a man at the motel -- leaving the guy with a fractured skull and a concussion -- and then fleeing the scene.

It's unclear what provoked the alleged attack ... but we're told Kennedy was eventually located and taken into custody.

During the booking process, though, the spokesperson says the skater became aggressive toward cops.

Kennedy allegedly threatened to murder officers NINE different times ... with the spokesperson saying Kennedy told cops, "I will kill one of you police. We kill police where I'm from."

The spokesperson says Kennedy then referenced a 2017 cop-killing incident in Whittier, CA. ... claiming the skateboarder said, "We killed ya'll in Whittier, California. We killed ya'll bitch ass."

Kennedy was ultimately arrested and booked on multiple charges including aggravated battery in a public place and threatening a public official, court records show.

The spokesperson said Kennedy had been out on bail due to a previous arrest earlier this month ... so he was also booked on a charge of violation of bail bond.

Kennedy showed up in court on Wednesday ... and his bail was set at $100,000, the spokesperson said. Jail records show the 36-year-old skater is still currently behind bars.

His next court date has been set for late August.

We've reached out to Kennedy's reps for comment, but so far, no word back yet.

Kennedy is one of the more famous figures in the skating world ... appearing in the "Skate" video game franchise as well as often riding at Dyrdek's fantasy factory.

In fact, back in 2010, Justin Bieber did a trick over Kennedy and Dyrdek at the famous skate spot.