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.