A bench of Chief Justice Dipak Misra and Justices A M Khanwilkar and D Y Chandrachud said it would not deal with the plea and asked the father to approach the High Court which would decide it by October 15.
Senior advocate P P Malhotra, appearing for the father, said crucial evidence was not being considered during the investigation.
The plea was filed during a recent uproar over the death of a 7-year-old boy in the toilet of Ryan International School in Gurgaon, who was found with his throat slit on September 8.
Gulshan Sehgal, father of the victim, has claimed in his plea that a probe by CBI or a special investigation team was required for a "thorough and fair investigation" as the school management has "already destroyed" evidence in the case.
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The plea said some members of the school management, including the chairman, director and principal, have moved the Allahabad High Court seeking quashing of the FIR and the court had granted them interim protection from arrest and directed that no coercive action should be taken against them.
"The high court failed to appreciate the fact that the police officials reached the scene of crime almost four hours late and by that time the school authorities had destroyed and tampered with crucial evidence," the petition, filed through advocate Gurmeet Singh, said.
It also alleged that the Uttar Pradesh Police had not probed the case properly, due to which the school authorities had tampered with the scene of crime and removed all evidence.
"The high court failed to appreciate the fact that the expert opinion suggests that the cause of death cannot be from a fall on the corridor and to the contrary, the expert opinion suggests that the injuries caused should be from a fall of atleast 20 feet height," the plea said.
The petitioner said even after 45 days of the incident, he does not know the reason and circumstances under which his son died.
He said on August 1, they had received a call from the school that his son had fallen in the corridor and was being taken to a hospital. But when he reached the hospital, they were told that the boy was declared 'brought dead'.
"The respondents deliberately and with criminal intent of mind, wiped away and caused to disappear all evidence pertaining to the occurrence. In this connection, it is submitted that the CCTV cameras were removed and so was the recording of the cameras," the plea alleged.