If the police says it wants to give you a warning, you can choose to
1) Accept the warning OR
2) Dispute the warning (which means, claim trial in court)
If you accept the warning, it means you have admitted to the offence and yes, you will have a record with the CID. However, this is not a so-called 'criminal record' in the true sense of the word, as you have not been convicted in a court of law.
This issue came out a few months back in the papers when someone got rejected when applying for a job because of this record of warning. He disputed it, saying he never committed the offence and that he had accepted the police warning out of convenience. The papers then interviewed a few lawyers who gave the advice that
one should never accept a police warning if he has never committed the offence as accused.
Perhaps you can seek the help from forumnites working in the police force?
They might be in a better position to clarify your doubts.
http://policeforce.sgforums.com