A simple question, but a big concern for me.

The Singapore immigration (MOM) has provided an EP card for me, as proof that I am working under a legal employment visa in this country.
I collected the card from my HR department, and asked them whether I still need to carry my passport around or not while traveling within the country.

The answer was NO, they said as long as I am only within the country, the EP card should be sufficient for my identification.

My concern is, in the past, this HR department has made a few mistakes related to my visa application and also my arrival arrangement, that's why I have doubt on their professionality.
I have also asked my foreign colleagues, but the answers vary, a few of them still carry their passports around all the time.

I am posting the question here in case someone can give a light into this or perhaps share their experiences.

In other different South East Asian countries though, based on my experiences, if we do not carry our passport along, the police will take advantages of us.
One case in Malaysia cost me to pay the police officers 100 MYR and another in Thailand for 500 Baht; thanks for high corruption level in South East Asian countries.

I believe Singapore is a clean and more straight country within this South East Asia region, and would like to avoid this kind of thing at all cost.

To summarize:

I am asking while I am in Singapore, do I still need to carry my passport around ? or can I just leave it in my Singapore home and only bring my EP card with me while still within Singapore territory ?