Addressing a press conference, Khan's mother and two sisters said Sharma was "like their family member" and alleged the deceased actor's mother used to force her to work even as Tunisha wanted to enjoy life.
A case under section 306 (abetment to suicide) of the Indian Penal Code has been registered against him.
Khan was produced in the court at Vasai in Maharashtra's Palghar district after his earlier remand ended. They needed more time to probe fresh allegations made by Sharma's mother, police told the court.
"It can be a case of murder. The act of Sheezan Khan getting Tunisha's (body) down and taking it to a hospital is doubtful. What happened in that 15 minutes needs to be probed," she said.
Sharma (21) was found hanging in the washroom on the set of a television serial near Vasai in Palghar district and Khan, her co-star, was held on December 25 for allegedly abetting her suicide. He is currently in police custody.
Tunisha Sharma, a television actor, died allegedly by suicide on set on December 24.
Sharma went to the washroom on the set and did not return for a long time. When the door was broken down, she was found hanging inside.