Justice S Vaidyanathan, who issued notice to Jayalalithaa's niece J Deepa and nephew J Deepak, said the court cannot order a DNA test as the petition's maintainability was yet to be argued.
If the petitioner's plea was accepted, "it will result in opening of a Pandoras box, which will only lead to more deterioration of the privacy" of Jayalalithaa, he said.
The apex court had, however, said she was at liberty to approach the high court.
Jayalalithaa died on December 5 last year after prolonged hospitalisation and her body was buried off the famous Marina Beach here.
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Referring to the petitioner's claim that late actor Shobhan Babu was her father, the judge asked why she had not sought a DNA test to prove it.
Replying to this, senior counsel V Prakash, who appeared for the petitioner, said she only wanted to establish her relationship with Jayalalithaa.
During the hearing yesterday, the judge, while noting that several persons were claiming that they were the legal hire of Jayalalithaa, had orally observed that a DNA test may be ordered to put the quietus on the issue.
Alleging that the petitioner was a 'fortune hunter' or 'publicity seeker', Advocate General Vijay Narayan had yesterday said that even for a DNA test, the court has to arrive at a prima facie case.