I vaguely recall reading an article summarising research that found that one of the overlooked methods of reducing crime in densely populated cities was better sound insulation.

The problem is that it rarely is a direct cause, except in rare crime passionnel situations. However, there's a measurable indirect effect when you add up the extra irritation, lack of sleep, etc. which affects all inhabitants of an apartment block. The consequences are measurable when you look at the "average".