Generally speaking, most conventional with less than a 50m range boomerang designs do not require special permits/airspace as they are by design physically not able to fly high enough to disrupt commercial/military air traffic.
Maximum Time Aloft (MTA) and Long Distance (LD) type boomerangs are not recommended within the context of Singapore to the much smaller open area sizes available outside of restricted areas.
Active SG (Fields)
https://www.activesgcircle.gov.sg/facilities/search?page=1&search=field