Former supermodel Viveka Babajee's family have so far not approached the police and registered a case of abetment of suicide against her boyfriend Gautam Vora.
The police said in case Viveka's family does not lodge a complaint against him, they would rely on witnesses and evidences to press charges.
The police said the family was in mourning and have not spoken to them yet.
"We will take their statements when they are in a position to talk," said ACP (west region) Amitabh Gupta.
Vora, a stockbroker has been in the media glare after Viveka committed suicide at her Bandra (W) apartment. A diary found from her house mentioned his name repeatedly with an entry that read, "You killed me Gautam Vora."
The police said the entry is not dated and is not enough evidence to charge him with abetment of suicide. Viveka's diary entries also reveal that her financial life was in turmoil.
The police, however, do not suspect any foul play in Viveka's suicide, but said the viscera report, expected in 15 days, would give them a clear picture.
The police have not recorded any detailed statements from anybody yet and will also check phone records of Viveka and her boyfriends.
Vora was untraceable since the day of the suicide.
On Monday, the sessions court granted interim-protection to him. He moved an application after media reports linked him to the suicide.
The court also directed the police to decide by Tuesday, after questioning him, whether they would be arresting Vora and tell the court. The matter will come up for hearing on Tuesday.
On Monday, Viveka's body was taken to Juhu crematorium for the funeral, attended by top models including Diana Soares and Carol Gracious.