Delhi Police, however, insisted it had done all it could, and had succeeded in ruling it out as a case of abduction.
Nafees, while welcoming the transfer, said though they wanted an independent inquiry into the case, the family was satisfied that it had been transferred to the premier investigating agency.
"The district police didn't do anything. When the probe was transferred to the Crime Branch, they didn't do anything either," she alleged.
The mother said the police "tarnished" Najeeb's image by saying that he suffered from an obsessive compulsive disorder (OCD).
"They kept saying that Najeeb had OCD when he was only undergoing treatment for insomnia. Even if he was depressed, that doesn't mean that the police could blame my son for his disappearance and not probe those who had beaten him up before he went missing," she said.
The investigators from the Crime Branch, however, said that the High Court had noted that the police had followed the court's directions.
They pointed out they had also traced the autorickshaw driver who had ferried Najeeb from JNU to Jamia on the day he went missing.
"There were many angles that we worked on and one of them was the abduction angle. But with the auto driver being traced, it emerged that Najeeb had left the university on his own," a senior police officer said.
Last week, the police had approached mosques in the national capital and UP, requesting them to make regular announcements about Najeeb, in the hope of making a headway.
They also wrote to the directors general (DGs) of police and prisons of all states and railway police, urging them to to share any information they might get about the student.
"It is a good move, but we were demanding an independent enquiry monitored by the court. Even the CBI functions under the ambit of the central government and can be influenced as we have seen in several cases," JNU students' union (JNUSU) president Mohit Kumar Pandey said.
A bench of Justices G S Sistani and Rekha Palli today transferred the case to the CBI responding to a plea filed by Nafees after Delhi Police said it had no problems with the case being moved.
The court said the probe by the CBI would be supervised by an officer, holding a rank not lower than that of a DIG.
The student went missing in October last year following a scuffle at his hostel with some students of the Akhil Bharatiya Vidyarthi Parishad (ABVP), a students' group affiliated to the ruling Bharatiya Janata Party.
ABVP leader Saurabh Sharma said he welcomed the move, but hoped the CBI would trace Najeeb and also unearth "his alleged links with the ISIS which Delhi Police has been hiding".
JNU Teachers' Association president Ayesha Kidwai urged the CBI to take up the search for Najeeb with an "earnestness" that "nobody, neither the police nor the JNU administration" had exhibited so far.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)