Singapore is one of the world's safest cities, full stop. Violent crime is extraordinarily rare. The main thing to know about safety in Singapore is its strict laws: chewing gum imports are restricted, jaywalking is fined, littering carries heavy penalties, and drug trafficking carries the death penalty. Ignorance of the law is not a defense — research Singapore's regulations before arriving.
The tap water is among the world's cleanest and perfectly safe to drink. Health facilities are world-class. The only real hazard is the occasional dengue fever from mosquitoes — use repellent, especially in parks.