Cox was taken into custody Thursday night following an investigation into an alleged assault reported Oct. 28 and brought to a Douglas County jail, said Michelle Kivela, public information officer for the city of Lone Tree, which is located about 20 miles south of Denver.
Cox appeared Friday in Douglas County Court in nearby Castle Rock wearing a gray prison uniform. His feet were shackled, and he was escorted by an armed sheriff's deputy.
A judge declined a defense attorney's request to reduce a $50,000 bond but did say that Cox can leave the state two times -- apparently to play in the Broncos' road games against the Arizona Cardinals this weekend and the Oakland Raiders on Dec. 19. Cox waived extradition, meaning he agreed not to fight transport back to Colorado if for some reason he were arrested out of state.
That means there's a 50-50 chance Cox will be in uniform for the game, but The Denver Postreported Saturday that the cornerback made the trip to Arizona.
The case filing was sealed at the request of the district attorney's office. Cox's next court hearing was set for Jan. 7.
Douglas County Court spokeswoman Casimir Spencer, prosecutor John Topolnicki and defense attorney Vince Buckmelter all declined to comment on the case.
When asked about the case, Cox's agent, Jordan Woy, said in an e-mail to The Associated Press on Friday, "We are still investigating the matter." He later added, "Perrish is meeting with the Broncos and we are dealing with this in a very serious manner."
"This is a serious matter and something we're taking extremely serious as an organization," Broncos interim coach Eric Studesville said. "We'll get all the facts together, get all the information we can, sit down and figure out what we're going to do based on the information we gather. It's disappointing news. Anytime you hear something like this, it always is."
Studesville was promoted from running backs coach late Monday after Josh McDaniels was fired in the midst of the franchise's worst skid in four decades and the videotape scandal that tarnished the team's image.
The Broncos, who are 3-9 and already have been eliminated from playoff contention for a fifth consecutive season, have been under a dark cloud all season, dealing with one ordeal after another.
Wide receiver Kenny McKinley committed suicide in September. Star linebacker D.J. Williams was stripped of his captaincy earlier this season following his second arrest on drunken-driving charges.
Cox has played in 11 games this season in place of Andre' Goodman, who might return Sunday from a leg injury that has sidelined him for most of the season.
A fifth-round draft pick out of Oklahoma State, Cox was coming off his best performance of the season at Kansas City last week and drew praise from his teammates and coaches for the job he did opposite Bailey in Denver's 10-6 loss.
"I don't truly know what's going on with him, so I can't truly comment. ... Whatever it is, I hope it's not a serious situation and he'll be back with us on Sunday," linebacker Mario Haggan said. "Unfortunately there's been adversity around this team this year. But I'm always optimistic that something good is going to happen in the midst of a storm."
The Associated Press contributed to this report.