The easiest way to get the police to handle this is to claim that you suspect the maid stole some kitchen knives and was behaving erratically before running away (on drugs?). She might just randomly stab somebody. Does MOM think you can track her down?
In any case, the rest of humanity has already moved on from using cheap slave labour through the use of automation and technology. Unfortunately, because most singaporeans have no love for engineering, we have never progressed beyond that. If the world was run by the PAP, we would still be in the middle ages.
Buying cheap labour from Myanmar is the trend now.