Rabia has alleged that Jiah was murdered and did not commit suicide as claimed by police.
The court was hearing a petition filed by Rabia, demanding a probe by Special Investigating Team or CBI into the actor's death as she produced forensic and medical evidence to indicate that it was a case of murder.
"You may approach the Police Commissioner with all your grievances and provide whatever evidence you may have in this regard", said the bench headed by Justice Naresh Patil while deferring the matter to May 8.
The suggestion to go before the police chief was given by public prosecutor Purnima Kantharia who vehemently denied the allegations of the petitioner that probe was improper and that an attempt was made by police to shield the accused.
Police had filed a chargesheet in the trial court naming Suraj Pancholi, son of Bollywood actor Aditya Pancholi, as an accused for abetting suicide of Jiah.
According to prosecution, both were into an intense relationship which was later severed.
Mahesh Jethmalani, counsel for Rabia, said his client wanted to know the truth and the cause of her daughter's death. She had procured evidence from private forensic experts which showed that Jiah did not take her life by hanging from the fan as claimed in the investigation but was murdered, he said.
Jethmalani also said that they were prepared to move the police commissioner with these grievances. He, however, asked for histopathology report and videography report of Jiah's postmortem which the police had not given them.
However, the judges opined that the Commissioner of Police may decide on this plea and asked the petitioner to come back to the court in case she was not satisfied with the response of the police establishment.
The prosecutor denied charges of petitioner that SMS messages sent by Suraj to Jiah just before her death were not part of chargesheet. She gave a copy of chargesheet to the court in which the text messages were part of the record.
However, Jethmalani said the SMS text messages were not appended to the copy of chargesheet given to Jiah's mother.
Prosecutor told the court that a laptop, an iPad and a cellphone of Jiah were sent to laboratory to retrieve the data and it would take about two to three weeks to get the information.
The prosecutor said videography of Jiah's postmortem formed part of 'Muddemal' (materials placed before the trial court). She said the trial court had rejected Rabia's plea to get a copy of this record.
Prosecutor Kantharia said the petitioner had conducted her own probe through some private agencies whose results were quite different from police investigation. Opinions were bound to differ, she said and asked Rabia to produce a list of things to show that the investigation by police was not proper.
This is the second time Rabia has approached the High Court. In October 2013, she had filed a petition seeking CBI probe but did not press for it as the court asked police to record her statement and probe as if it was a case of murder.
The police had probed on these lines and filed a chargesheet saying it was a suicide case and charged Suraj Pancholi, Jiah's boyfriend, for abetment of suicide.
Jethmalani argued that he was asking for a fair and transparent probe.
Rabia (53) has cited circumstances which, she claims, indicate that Jiah was killed. The air-conditioner in Jiah's bedroom was on but windows were open when she was found dead. Also, there is no explanation as to how Jiah reached the ceiling fan to hang herself when there was no stool in house.
Blaming Suraj for her daughter's death, Rabia said she had carried out a sting operation of few witnesses who said in an audio recording that they had not told police what had been recorded in their statements, thereby doubting the police version that Jiah had committed suicide.
Rabia alleged that the police had ignored the opinion of a forensic expert sought by her. The expert had opined that the injury mark found on Jiah's person was circular which is impossible in a case of suicide.
The expert had also pointed out that the injury marks were so prominent that the same could not have been possible if a muslin 'dupatta' was used in the crime. Also, the injury mark had two prominent outer lines which are running parallel to each other which is possible if a belt was used. Besides, injury marks on the lip, chin hands and the neck of the deceased are not been explained at all.