The woman told investigators that doctors put the date of conception around the time she went to Cox's apartment with friends in the early hours of Sept. 6, according to the arrest warrant affidavit.
The affidavit said DNA tests indicated Cox was the father.
The woman said she has no recollection of most of that night and wasn't sure anyone had sex with her until she learned she was pregnant. She said she hadn't had consensual sex for several weeks before or after the date of conception reported by doctors.
The woman said she and Cox's girlfriend at the time had gone to a club Sept. 5, and they met Cox and Broncos wide receiver Demaryius Thomas. When the club closed at 1:30 a.m., they all went to Cox's apartment. She said Cox's roommate, Broncos defensive back Cassius Vaughn, was there when she awoke later in the day.
The woman said she believed she had been drugged because she felt unusually woozy after four drinks. She said she recalled being kissed and fondled by Thomas before she passed out.
Thomas told police he had kissed the woman, according to the affidavit. He didn't immediately return messages Friday.
Cox's lawyer, Harvey Steinberg, declined to comment on any of the information in the arrest affidavit.
"My thoughts have always been that cases work their way through the court system, and we need to do our best to ensure people who are charged get fair trials," he told The Associated Press. "I'm just hopeful the process works."
When police interviewed Cox on Nov. 8, he denied having sex with the alleged victim, the affidavit said.
As he left the courthouse after hearing in May, Cox said: "It's tough. It's something that stays over your head. You stay positive and just control what you can control." He has made few other public comments.
Craig Silverman, an attorney for the woman involved, issued a statement insisting that his client "suffered a sexual assault by Perrish Cox."
"For her, this is an intensely painful, personal and private matter," Silverman said. "My client's victimization will be made clear in a court of law."
The woman went to police Oct. 28, the day she said she learned she was pregnant. She said she didn't file a complaint sooner because she wasn't sure she had been raped and didn't want to make unfounded charges.
The affidavit said the woman was shocked when DNA results came back Nov. 29 indicating Cox was the father.
Cox refused to allow a DNA sample to be taken until after investigators obtained a court order, the document said.
The affidavit says Thomas voluntarily provided a DNA sample, and Vaughn provided one after police obtained a court order, but it wasn't clear if he refused to volunteer one. The affidavit said DNA tests ruled both of them out as the father.
Steinberg had fought to keep the affidavit sealed, but The Associated Press and The Denver Post asked the courts to release it. Steinberg appealed to the Colorado Supreme Court when a judge ordered the affidavit made public, but on Friday, the high court refused to take the appeal and the affidavit was released.
Steve Zansberg, an attorney who represented The AP and The Post, called the Supreme Court's decision "a victory for the peoples' right."
"This is about the people's right to monitor and scrutinize the conduct of government institutions," he said.
Cox, 24, was arrested Dec. 9 and pleaded not guilty to one count of sexual assault while the victim was physically helpless and one count of sexual assault while the victim was incapable of determining the nature of the conduct.
Cox is free on $50,000 bail. His trial is scheduled for October.
The Broncos fined Cox in December for missing meetings and practice after his arrest. The team didn't release the amount of the fine but said it was the maximum.
Cox could face a four-game suspension from the NFL next season for violating the league's personal-conduct policy. NFL Commissioner Roger Goodell doesn't need a player's conviction to impose punishment.
Copyright 2011 by The Associated Press