For starters, unlike in the West where there is an Inheritance Tax, there is no tax payable on inherited property or estate in India.
In some countries like Japan, France, Switzerland and a host of others, there is either an Inheritance Tax or an Estate Tax that is applicable. Both the set of taxes differ in the sense that an Estate Tax is levied on the assets of the deceased, while an Inheritance Tax is assessed on the legacies received by the beneficiaries of the estate.
In India, whether you are a resident Indian or a NRI, you need not pay Inheritance Tax. But, there are other taxes that you might end-up paying. For example, if a NRI sells the inherited property, then you are liable to pay capital gains tax, if you have made profits on the sale of the property. You have to first ascertain the cost of the acquisition of the property and then the sale price to determine the capital gains and pay tax accordingly.
Similarly, if you rent the property, then the rental income has to be added and you are liable to pay Income Tax in India.
Now, if you already own a apartment and inherit another, you own two apartments. This means, even if you do not rent both, one of the flats would have to be deemed to be given on rent, whether you rent the same or not. From the rental income so derived, you can deduct municipal taxes actually paid and a fixed allowance of 30 per cent of the rent.
You also need to pay wealth tax on one property on the valuation to be done.
Though there is no Inheritance Tax in India, you may end-up paying some tax or the other indirectly depending on your action. Careful planning and professional advise is necessary to ensure you have proper tax planning. There are reports that the government may in the Union Budget look at the possibility of re-introducing Inheritance Tax. One will have to wait for July 10, when Finance Minister Arun Jaitley will introduce his maiden Union Budget.