However, it said, the CBI can conduct the polygraph test on controversial arms dealer Abhishek Verma, a witness in the case, as he consented to it.
Additional Chief Metropolitan Magistrate Shivali Sharma directed the concerned deputy commissioner of Delhi police to provide round-the-clock security to Verma till the time he undergoes the test, after which the threat perception would be re-assessed.
The court also allowed advocate Maninder Singh, who appeared for Verma, to remain present during the test.
The court also asked the IO to inform it of places where the facilities to conduct the test are available.
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During the hearing, the court recorded Verma's statement giving consent to the test, in which he endorsed his earlier statement given to the CBI against Tytler.
While Tytler has refused to undergo the polygraph test, Verma gave conditional consent, saying he is ready to undergo the test if provided with round-the-clock security, as he fears threats to his life.
The CBI's IO also said they have no problem if Verma is provided security round the clock till he undergoes the test.
The CBI's move seeking permission to conduct the polygraph test on Tytler and Verma came after the court's December 4, 2015 order in which it was mentioned that such a test may be conducted, if required.
Tytler, who has denied any role in the riots, was thrice given a clean chit by the CBI in the case, but the agency was directed by the court to further investigate the matter. The victims had filed a protest petition challenging the CBI's closure reports in the case.
The court had on December 2015 directed the CBI to further investigate the matter and decided to monitor it every two months to ensure no aspect was left uninvestigated.