I thought custom duty only applies to real things that you physically imported
the regulation of declaring $10,000 is for anyone carrying physically dollar bill or traveller cheques into the US
having offshore account has nothing to do with custom but should be included (declare) in your tax report
the question is whether the money in that offshore account is legit and already taxed?
since bitcoin is digital money or treated as virtual commodity in some countries
I don't think there should be any declaration as in custom duty
Let's say, the Crypto was bought in USA, and the person bought it, is going to move to India permanently.
I have little knowledge on procedures and laws on this, but do you mean permanently here as in changing citizenship?
if you simply move for work without that intention (will return to US someday), then you are still under US citizen law
though the income tax matter, you need to read more on US/India tax treaty agreements
as in real income from your job and realized capital gain from bitcoin trading