District Court Judge Paul King granted a request Wednesday from Cox's lawyer to delay release to give him time to appeal to the state Supreme Court.
Cox is accused of two counts of sexual assault stemming from a Sept. 6 incident. Cox has pleaded not guilty.
Such affidavits are often available to the public, but in January the judge ordered that it be kept secret, saying it could expose Cox and the alleged victim to abuse.
The Associated Press and The Denver Post asked the judge to reconsider and he granted the request last week. He said the alleged victim's name and other personal information must be redacted before it is released.