The police are assessing the actor's financial status and business dealings to identify the cause of his depression.
Sushant Singh Rajput's father Krishna Kumar Singh has told the police that he and other family members did not know the cause behind his son's depression, a police officer said.
The police have so far recorded statements of nine people, including Singh and his two daughters.
Their statements were recorded on Tuesday before they flew to Delhi after performing Sushant's last rites, the officer said.
In his statement, K K Singh told the police that family members were unaware about the cause of the actor's depression.
"So far we have recorded statements of nine persons, including the actor's cook, a caretaker and managers," a senior police officer said.
Sushant was found hanging inside his apartment on Sunday. No suicide note was found at the spot.
The police are also looking into whether Sushant was depressed due to professional rivalry.
Investigators, the police officer said, are clueless about the trigger for the actor taking the extreme step.
"We are speaking to the people who were close to the actor," he said.
When asked about the course of investigation, the officer said the police are assessing the actor's financial status and business dealings to identify the cause of his depression.
Maharashtra Home Minister Anil Deshmukh had said the Mumbai police will probe the alleged cause of 'clinical depression owing to professional rivalry' behind Sushant's suicide.