The Constitution of India gives single citizenship to the people of the country.
All the people irrespective of the states or territories in which they reside are the citizens of the country.
This is unlike USA, where a citizen is a citizen of USA and the state in which he/she resides.
Fourteenth Amendment, Section 1: All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
However, up until 4 April 2002, the previous Australian Citizenship Act 1948 (the old Act) did contain an automatic loss provision (section 17 of the old Act) by which an adult who acquired the citizenship of another country may have automatically ceased to be an Australian citizen.