No arrests have been made in the case so far.
The incident had occurred on Tuesday morning at about 9.30 am when 27-year-old Shruti Haasan, daughter of noted actor Kamal Haasan, answered the door bell of her sixth floor apartment in a building at Bandra West, the police said.
She was confronted by a stalker who allegedly tried to barge into the apartment and also asked her why she had failed to "recognise" him.
"The accused had even put his hand on the actress' shoulder. Although she was rattled, she managed to push the man away and lock the door," a police officer said.
"A shocked Shruti lodged the complaint late last night. The accused was booked under Section 354 (assault or criminal force on woman with intent to outrage her modesty) and Section 452 (house trespass after preparation for hurt, assault or wrongful restraint) of the Indian Penal Code," Assistant Police Commissioner Shivaji Kolekar said.
According to the actress, the accused was spotted on the sets of her films on a few occasions before Tuesday and also seen at Mehboob Studio as well as Film City studio where she had shot earlier.
"We have obtained CCTV footage of the residential building. The man is seen in the footage and we are in the process of identifying him. The accused had made an entry in the building's visitor diary as 'Ashok' but it may be a fake name," a police officer said.