Official sources told Dawn on Sunday that Home Secretary Abdul Kabeer Kazi has been informed by the police about sessions judge's reluctance to initiate the inquiry.
Another source said: "We have learnt that the sessions judge has outright declined to hold the inquiry".
According to the source, Kazi was said to have told the Larkana police that the sessions judge was supposed to put it in writing if he was not willing to initiate the inquiry.
"Things might get clear on Monday," the source told Dawn news.
Nimrita Kumari's body was found on September 16 hanging from the ceiling fan in her hostel room at the Shaheed Mohtarma Benazir Bhutto Medical University (SMBBMU) in Larkana, Sindh province.
She was enrolled in the university's Bachelor of Dental Surgery programme and was a final year student.
The Larkana police, meanwhile, remained in a fix. "Neither the (vistim's) family is coming forward to lodge an FIR of the incident nor are the police ready to register a suicide case," said the source.
Police have been keeping two students - Mehran Abro and Wasay alias Ali Shan Memon - in custody for several days for questioning.
Abro, one of the 32 accused persons in the case, was taken into custody on September. He has claimed that the victim was in love with him and wanted to get married.
The police had earlier said that it was it was too soon to confirm whether the death was due to suicide or murder.
Meanwhile, Dawn news said in a report last week that experts and officials of the medico-legal section of the Karachi health department have raised doubts over the victim's initial autopsy report.
The experts believed the report carried many flaws and missed key facts, including that the ligature mark on her neck was not due to a 'dupatta' (scarf) but "it was some rope material".
They also said that it was also questionable as to how a five-feet-tall girl managed to hang herself from the ceiling fan, which was 15 feet high.
( With inputs from IANS )