Tytler's counsel objected to the test, saying the CBI has not given any reason for conducting it and the agency's plea for the test was a "gross misuse of law" and it was filed with "malafide intention".
He also filed a list of events since the riots broke out till now to which the victims' counsel said they would a reply to it.
The move came in pursuance to the court's December 4, 2015 order in which it was mentioned that lie detection test may be conducted, if required.
Verma, a witness in the case, also told the court that he was ready for the polygraph test if he is provided with adequate security as he apprehends threat to his life as well as to his family.
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The CBI prosecutor, however, did not agree with the proposal of recording Verma's statement and said the consent for polygraph test should be unconditional.
Advocate Prabhsahay Kaur, who represented the victims, questioned the CBI as to why it was refusing to record the statement when the witness was ready for it.
She also said that the witness should be given proper security if he apprehends threat to his life.
Meanwhile, the CBI filed a status report before the court in a sealed cover regarding its further probe in the case.
Tytler, who has denied any role in the riots, has been given a clean chit by the CBI thrice in the case but the probe agency has been directed by the court to further investigate the matter.
Verma has made several statements to the CBI against Tytler that he allegedly pressured the witnesses in the case.
The court had in December 2015 directed the CBI to further investigate the matter and had said it would monitor the probe every two months so that no aspect is left uninvestigated.