Police said the alarm was raised at 5.48am on Sunday August 9 when a woman was heard shouting out from a house in Adelaide Road, Chichester.
A Sussex Police spokesman said: ‘She had woken up to find a man holding her by her shoulders. She screamed and he ran back out of the door through which he had entered.’
Police said the 'apparent opportunist intruder' took advantage of a door, which had been left insecure, before 'assaulting a woman inside'.
The spokesperson added: ‘He is described as white, in his 20s, around 6ft and wearing a dark T-shirt, black or grey jogging bottoms and trainers.
‘The woman ran outside and saw a person get on to a moped or motorbike about 100 yards up the road. However, she is not sure that it was the same man and it could be that that person could be an important witness.’
The woman's handbag, containing her passport, student card and cash was stolen from the property, police said.
Inspector Sharon Sawyer said: ‘This was obviously a very alarming experience.
‘While the man's intentions are not known, it may be that he entered the house with a view to burglary and was diverted by the presence of the victim in her bed.
‘In this hot weather, however, it does reinforce the need to ensure that if you do leave windows or doors open to keep cool, they should be suitably secured to prevent unwelcome intruders.
‘This applies as much to an unattended room or area in daytime as much as during the night.’
Anyone with information about the incident is asked to report online or call 101 quoting serial 373 of 09/08.