I heard that if my business is dormant and need not file an income tax return at all. Is that true?

That is incorrect and is a myth. It is also important to note that the definition of dormant for ACRA and IRAS is different. IRAS definition of dormant is that it does not carry out business and has no income for the whole of the basis period.

A dormant company in fact must still file its income tax return unless it has been granted the waiver of income tax return.