The case relates to massacre at Gulberg Society here during the post-Godhra riots. As many as 69 persons, including former Congress MP Ehsan Jafri, were killed in the incident.
"We want to undergo narco and brain mapping test with our own consent and without being in fear or under pressure of any other persons," said the application filed by Babu Rathod alias Babu Marvadi and Naran Tank alias Naran Channelvala before judge P B Desai.
Terming the investigation as biased, the two accused contend that they were framed up. The application also says that they may file a petition for further investigation in the case as per the direction of the High Court.
The court, which is conducting final hearing in the case, is likely to hear the application next week.
The Gulberg Society case is one of the nine cases of the 2002 Gujarat riots probed by the Supreme Court-appointed Special Investigation Team. There are 66 accused in the case.