It depends on your residency status when you had your first account. If you were not an NRI before, you would have to close your regular Demat account and start a new NRI account and a Portfolio Investment Scheme account as a pass through.
If you were an NRI, you can transfer both your PIS and Demat accounts. e.g. if I had a PIS account with Axis and an NRI Demat account with Angel Broking, and I want both to be transferred to ICICI, they list the procedure as follows:
http://content.icicidirect.com/nrifaq.asp#a32
7.2
What if I want to switch my exiting NRE and NRO account under PINS to ICICI Bank?
In such a case, you need to close your investment activities through existing NRE and NRO account and open new accounts with ICICI Bank. You need to apply to your existing designated bank to issue the necessary ‘no objection certificate’ which would give details of the latest status of your portfolio as on the date of the issue of ‘no objection certificate’.
The ‘no objection certificate’ issued by your existing bank along with previous approval document in original should be submitted to ICICI Bank. Based on the securities, cost of acquisition and date of acquisition mentioned in the certificate, ICICI Bank will create record of your portfolio in its books.
ICICI bank would open your NRE and/or NRO accounts, but the same shall be designated as accounts under the Portfolio Investment Scheme only after receipt of the ‘no objection certificate’.
7.3
What is the previous approval document?
If you an existing PIN relationship with any other Bank in India, you would have already an approval from RBI for the same. This permission/approval would have been taken by your bank on your behalf. Such permission or approval is referred as previous approval document.
7.4
Do I need fresh approvals under PINS after switching from existing bank to ICICI Bank?
Yes, you need to have fresh approvals, as the earlier approvals will no longer be valid. ICICI Bank itself would issue the necessary approval in this regard and you need not fill in any separate request/application for the same.
7.5
What if I already have a Demat account with other Depository Participant?
To avail of the advantage offered by the integration of the brokerage, Bank and the Demat account, all the three accounts will have to be opened with ICICI group. You can transfer your holdings from these accounts to the new Demat accounts opened with ICICI Bank.