Sussex Police also believed he touched another woman in the street shortly after the incident, which happened near Crawley, West Sussex.
A statement from the force said: "At about 4pm on Friday, July 12, a man called at a woman's house in Newtown, Copthorne, and asked where the nearest bus stop was. He then barged his way in and touched her. She pushed him out and locked the front door. He then carried on knocking on the door before leaving.
"Officers responded immediately and carried out a search of the area but could not find the man. A short time later another woman reported that a man had approached her asking for a hug and then touched her as she tried to get into her car in Knowle Drive, Copthorne, at about 4.05pm. She shouted at him and he ran off."
Police described the suspect as white, aged about 20, 5' 9", slim, with light brown hair and was wearing a white buttoned up shirt, dark trousers and carrying a dark coloured backpack.
Detective Sergeant Joel Brooks said: "These incidents were frightening and distressing for the victims and we are keen to hear from anyone who may have seen this man hanging around or approaching the women.
"We are carrying out searches, making enquiries and have police officers in the area."
If you can help with the investigation please report online or ring 101 quoting serial of 1078 of 12/7.