It has sought setting aside of the 2014-15 guidelines on the ground that the LG office lacked the power to frame them.
It claimed the guidelines were against the principle of autonomy and the recognised unaided private schools were given the power by the Central government to formulate their own admission criteria for 75 per cent seats.
Central government, the Directorate of Education (DoE) and the office of LG have been made party in the plea.
Lieutenant Governor Najeeb Jung, on 18 December, issued new guidelines for the nursery admissions for the session 2014-15 and took various steps such as scrapping of 20 per cent management quota.
The neighbourhood criteria, which seeks schools to give preference to children living within the radius of six km from school, has been given maximum weightage with 70 points out of 100 in the open category seats.