With effect from 1 May 1999, if you are involved in a non-injury motor accident in Singapore, you do not need to make a police report unless your accident falls in 5 categories of exception. In all non-injury accidents, you must make a report to your insurance company. For more details on the Non-Injury Motor Accident Report Scheme, please go to the section on the same on the GIA web-site.
Source: GIA