Under the jurisdiction of the local bishop. That is Canon Law.
That same Canon Law does not allow laymen to hire and fire priests, nor to disobey the local bishop.
I'd certainly favor more control of local churches by the laity. But, in a civil dispute such as this, governments will defer to the ecclesiastical jurisdiction, and that is the local bishop.
The Mission does participate in a division of its Sunday collection with the Diocese Office, and promotes the annual pledge to the Diocese Fund.
Likewise a Catholic university lies within the Diocese, but the lay faculty answers to the Jesuit Order - who also own the property.
Actually more complicated than that. The current Code of Canon Law expects the Church to live within the civil code where it finds itself, in general. The case in India varies from state to state where there are political realities for parishes that require a Catholic bishop to function in a way that no American bishop could imagine. The bishop in this case is doing what most Catholic bishops are doing in India, smashing and destroying the old civil structures that bound them by using whatever means are necessary. This has been happening since the Council and has been ratcheting up in recent years to a fever pitch in several parts of India.
Game over.
The laity already control the local church already. In my town they decided baptism is not necessary, and that's that.