Can an NRI have both, Resident and NRI Bank Account in India?

No, NRI's are not permitted to have resident saving account in India. The resident saving account should be converted to NRI account as soon as the status of person changes to Non-Resident. This is as per the RBI and Income Tax laws for NRIs.

Technically an individual cannot hold both the status i.e. resident and non-resident at the same time.

If the individual is an NRI, he needs to close the resident saving account and open NRI account.

If the individual is a resident Indian, then he needs to close the NRI account and open a normal saving account.