According to police, Swarnakar managed to get the mobile phone numbers of Bhatt and her film maker father Mahesh Bhatt from his neighbour Dhruv, who is a music composer.
On Wednesday, Pooja Bhatt had lodged a complaint with Bandra police station stating that she was receiving obscene and threatening calls from an unidentified person.
The caller had rung up Mahesh Bhatt as well but he did not attend the calls as his phone was on silent mode, police said.
As cops were trying to track the mobile number from which the threatening calls were made, the accused kept changing the locations and switched off his phone many times, making it difficult for investigators to trace his location, Deputy Commissioner of Police Pratap Dighavkar said.
Police said that they would be checking whether Swarnakar, who has no past criminal record, had made similar calls to any other celebrities.
Swarnakar made three calls on Pooja's mobile phone but did not make any monetary demand or try to extort money from the complainant and has no connection with the family or their movie business, police said.
Swarnakar, who has been booked under section 507 (criminal intimidation by anonymous communication) and 509 (word, gesture or act to outrage the modesty of a woman) of IPC, was produced in the court on Saturday which remanded him to judicial custody.