They say it happened in the early hours of Tuesday 7th October in the South Belfast area.
RCU Detective Sergeant Mike Davis said: “We are appealing to members of the public to assist us determine the movements of a 20 year old woman in the South Belfast area between midnight and 4am on Tuesday morning.
“The woman is around 5’1” tall, of slim build with waist length dark hair and was wearing a white dress with blue and green flowers on it, silver high heel shoes and was carrying a black shoulder bag.
“We would ask anyone who saw a woman matching this description in the University Terrace, College Gardens, Lisburn Road or Tates Avenue area anytime between midnight and 4am to contact detectives at the Rape Crime Unit on 028 90 700305.
“Or if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”