One succession proceeding, not one per state
For accounts, deposits and securities, the document usually needed is a succession certificate, and jurisdiction to grant it sits with the District Court where the deceased ordinarily resided at the time of death (Section 371 of the Indian Succession Act). Only where the deceased had no fixed place of residence does the court where the property lies come into play.
Crucially, a succession certificate granted by the competent court has effect throughout India (Section 380), so a single certificate from the residence court generally reaches the deposits and shares held in other states. You do not normally file a fresh certificate in each state where an account happens to sit. A practising CA and your lawyer identify the right court once and use the resulting certificate across the estate.
Where there is a will, the probate rule has changed
If the estate passes under a will, the position changed recently and materially. Until the end of 2025, a will made by a Hindu covering property in the major metro jurisdictions often needed probate before an executor or legatee could act on it. The Repealing and Amending Act 2025 has omitted the section that required this, so probate is now voluntary rather than mandatory.
That removes what used to be the biggest multi-state headache, the prospect of separate probate proceedings. In practice a bank, registrar or housing society may still ask for a grant before transferring a particular asset, and where they do, an Indian court can recognise a foreign or out-of-state grant on an authenticated copy rather than re-proving the will (Section 228). So the will route across states is now far lighter than it was.
The tax side is one central return
Whatever the geography of the assets, the income-tax side does not fragment. Income tax in India is a central levy, so there is no state-level income-tax filing to duplicate. The rental income from the flat, the capital gain when you sell the land, and the interest on the deposits all go into a single return on your own PAN.
When you eventually sell the inherited properties, each sale carries the previous owner's cost and holding period (Section 49(1) and Section 2(42A)), and the TDS the buyers deduct under Section 195 is claimed together on that one return. So a scattered estate produces one tax filing, not one per state, which a practising CA assembles from the Indian side.