Constitutionally NO.
The National Register of Citizens (NRC) is a citizenship subject that falls in the Union List of the 7thSchedule of the Indian Constitution.
NRC will be a Union Subject and the state governments are mandated to implement it as the Government of India keeps the Constitutional Authority to implement it throughout the Country.
If some state governments refuse to block the NCR process, then the Government of India can invoke Article 256 of the Indian Constitution to direct the state governments to implement the act.
Article 256 ensures compliance of the laws made by the Parliament.
Practically, YES.
The NRC process is going to be heavily dependent of the state’s manpower, unlike the Citizen Amendment Act (CAA), where the Union Government can try to find an alternate route to process the CAA applications as the process requires a limited number of people. It can, it fact, think of establishing offices run by it across India like it happens in a passport application process and can outsource the investigation to the central agencies.
Law and order are state subjects and after seeing protests and violence against CAA, and people linking CAA to NRC, the state governments can refuse to start the process.
The state governments can refuse to operationalize their manpower for the NRC process and without their involvement, the NRC process can’t move ahead.
The state governments can invoke the Original Jurisdiction of the Supreme Court under Article 131 of the Indian Constitution. They can file an Original Suit against the Union Government with a demand to strike down the NRC process.
Article 256 – Obligation of States and the Union
The executive power of every State shall be so exercised as to ensure compliance with the laws made by Parliament and any existing laws which apply in that State, and the executive power of the Union shall extend to the giving of such directions to a State as may appear to the Government of India to be necessary for that purpose.
Article 131
Original jurisdiction of the Supreme Court Subject to the provisions of the Constitution, the Supreme Court shall, to the exclusion of any other court, have original jurisdiction in any dispute,
between the Government of India and one or more States; or
between the Government of India and any State or States on one side and one or more other States on the other.