Tell you something that the Police have never revealed and which solves 95% of cases in the past. GD has also hinted.
The moment it become evident that its a potential case and SIS is called, detectives will go straight to Singtel/Phone companies and download all logs of victims phones (mobile, home, office etc). Typically the last contact is more likely to throw light on the case or is involved in the case. They go straight for the person or person and these guys are just stunned by quick appearence of the Police and the body language gives the game away.
The trouble is when no phone is involved or when unknown person to the victim is involved. For gang related murders from sudden fights, they will call the headman for the area. Within hours, they will get their answer even if it is a fellow gangmember. Obviously the headman is not going to reveal that he identified his own member. If the headman does not help, totall harrassment will take place.
Fingerprints, DNA are all secondary but very important secure conviction in court.