Justice Vibhu Bakhru issued notice to the Ministry of Health and Family Welfare, Delhi government and Lok Nayak Hospital, where the girl is admitted, and sought their replies within four weeks.
It directed them to meanwhile continue providing free treatment to the 13-year-old girl child who suffers from the genetic condition that only affects females and is caused by an abnormal sex chromosome.
The court was hearing a petition filed on behalf of the minor girl, through advocate Ashok Aggarwal.
The petition states that the girl's father is a tailor and sole bread winner in the family of four and earns around Rs 7500 per month, while the monthly cost of treatment of the child is Rs 15,000.
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The child is undergoing growth hormone therapy which needs to be continued for three-four years, the petition has said.
The petition also stated that the girl was not found eligible for aid under the Delhi Arogya Nidhi Scheme "for want of three years domicile" in the national capital.
It further stated that Rs 50,000 was sanctioned from the Prime Minister National Relief Fund towards her medical expenses with which four months medication has been procured and added the same will be exhausted by the end of this month.