Sahil Malik falls unconscious every time he is questioned, police said.
Police arrested Rinky's boyfriend Sahil Malik on Oct 30 and booked him for murder charge.
Earlier, on Nov 2 Mumbai police questioned Sahil Malik's ex-girlfriend Shyamli Jain aka Princy.
Police arrested Princy after Sahil malik blammed her for creating rift between him and Rinky. He also claimed that Princy used to call Rinky frequently and preventing her from marrying Sahil.
Now the investigators are trying to locate Sahil's friend Shivendu Shekhar, who had visited Rinky's flat on the day of the incident.
Shivendu left the city after the incident. A police team has left for Shekhar's hometown in Rajasthan.