The petition referred to the recent statement by Asaram's son Narayan Sai that the minor girl was "mentally unstable" and said there was "low implementation" of the Juvenile Justice Act, 2000.
"Direct a Supreme Court-monitored CBI probe into the incident involving the rape of minor by Asaram Bapu in the Jodhpur Ashram premises ...," Chennai-based D I Nathan said in his PIL filed through advocate N Rajaraman.
It also said the Home Ministry should be directed for immediate scientific test for ascertaining the biological age of victims, who are children, and fast tracking of the probe so that evidence was not obliterated.
The petitioner said the object of the Juvenile Justice Act, 2000 was "repeatedly violated and disregarded by the police, state authorities and the accused who are violating the privacy and the right to life of minor victims."
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It said sensitivity of the police investigating crimes against the juvenile victims and the media, which is reporting such crimes against the victims, were violating the purpose of the Act.
Asaram had sought extension in the date of appearance before the investigation officer of the case at Jodhpur citing he had various pre-decided religious fixtures lined up till September 19.