After protests, the Gujarat Government set up an inquiry commission, which submitted a report in July last year but its contents have not been made public.
The application was filed by Dipesh's father Praful Vaghela before Chief Metropolitan Magistrate S V Parekh, who kept the matter for hearing on February 28.
The aggrieved parents had demanded a probe by the Central agency earlier also.
In the latest plea, they said the cause of the kids' death had not been investigated properly by the local police as well as the commission headed by Justice D K Trivedi.
All investigations till now, according to the applicant, have been aimed at shielding the real killers of the children.