A bench of Justices M B Lokur and Deepak Gupta also refused to allow the plea of the woman to conduct DNA test for the purpose of proving her parentage.
Senior Advocate Indira Jaising, who appeared for the woman, had also sought cremation of Jayalalithaa as per Hindu rites since she was an Iyengar Brahmin.
The court, however, said the petitioner is at liberty to approach the high court.
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