Union Territories & Panchayats
(1) Since 1991, Delhi is called the National Capital Territory of Delhi, with its administrator designated Lieutenant Governor. (2) Delhi has a directly-elected Legislative Assembly. (3) The Assembly can make laws on State List and Concurrent List matters applicable to Union Territories, EXCEPT police, public order, and land (Entries 1, 2, and 18 of the State List) - Parliament's own law-making power isn't affected, and a Union law prevails over a conflicting Assembly law unless the Assembly's law was reserved for and received the President's assent. (4) A Council of Ministers (up to 10% of Assembly membership), headed by the Chief Minister, aids and advises the Lieutenant Governor - except where the Lieutenant Governor must act in their own discretion, and disputes between them go to the President for a binding decision (with the Lieutenant Governor able to act urgently pending that decision). (5)-(6) The Chief Minister and Ministers are appointed by the President, and the Council of Ministers is collectively responsible to the Assembly.
Delhi occupies a genuinely unique constitutional position - it's a Union Territory, not a full State, but has its own elected Legislative Assembly and Chief Minister, unlike most other Union Territories. Crucially, though, Delhi's Assembly is specifically barred from legislating on police, public order, and land - these remain with the central government, which is why Delhi's own elected government has historically clashed with the Lieutenant Governor (representing the Centre) over the boundaries of their respective powers, especially concerning administrative services.
This is why control over the Delhi Police remains with the central government rather than Delhi's own elected Chief Minister, unlike in a full State where the state government controls its own police force - a frequent source of friction given Delhi's unique "neither full State nor ordinary Union Territory" status.