Delhi as earlier a Union Territory. Now, the process has been initiated to give Delhi the State-hood. However, as Delhi is the capital of India, some of the powers of states are being exercised by the Central Government in respect of Delhi. As for example, law & order is a state subject, but in case of Delhi, it is being exercised by the Central Government. So, Delhi Police is under Central Government.
Delhi Legislative Assembly was re-established in 1993 (after abolition in 1956), after the Constitution (69th Amendment) Act, 1991 came into force, followed by the Government of National Capital Territory of Delhi Act, 1991. The 69th Amendment to the Constitution of India declared Union Territory of Delhi to be formally known as National Capital Territory of Delhi.
So, we can state that Delhi is a semi-state under a Lieutenant Governor and a Chief Minister with a 70 member Legislative Assembly.
Caution: Explosive. Handle with care.