"We believe through the investigation and our evidence that his claim is just not correct," St. George Police Sgt. Sam Despain told HuffPost.
Kelly made his first appearance in court on Monday but did not enter a plea.
According to the Tribune, police responding to an emergency call on May 19 found Kelly giving CPR to the 29-year-old woman, with whom he had a previous relationship. The woman suspected she had been raped because of bruises on her thighs. Her vaginal area had allegedly been cleaned, preventing the hospital from completing a rape kit.
Kelly's next court appearance is scheduled for June 17.