Singapore has a very low crime rate; it's safe to walk around unaccompanied at night and people often leave their bags unattended. Bear in mind, however, that low crime doesn't mean no crime. Be watchful of your handbag in busy pedestrian areas and packed trains. Don't wear a money belt or a waist pack, both of which peg you as a tourist. Distribute your cash and any valuables (including your credit cards and passport) between a deep front pocket, an inside jacket or vest pocket, and a hidden money pouch. Do not reach for the money pouch once you're in public.
Jaywalk at your own risk; Singapore drivers won't slow down or stop to let you cross.
If you carry a purse, choose one with a zipper and a thick strap that you can drape across your body; adjust the length so that the purse sits in front of you at or above hip level. (Don't wear a money belt or a waist pack.) Store only enough money in the purse to cover casual spending. Distribute the rest of your cash and any valuables between deep front pockets, inside jacket or vest pockets, and a concealed money pouch.
In general, attitudes toward women are fairly liberated and relaxed. You're unlikely to be hassled. Men on the prowl generally avoid public confrontation and will retreat at the first loud reprimand.