1. Supreme Court in ONGC case and Conservator of forests Case held that litigation between two limbs of govt. organisation is to be decided by an empowered committee formed by secretaries of concenred departments but not by way of litigation.
2. In view of Art.131 of Constitution of India, Supreme Court has exclusive jurisdiction over litigation between two States.
In view of Supreme Court's decisions, I feel filing of a writ petition is not the proper solution.