DC does a reasonable job of dealing with crime. The main issue is that with wealth inequality the poorest people can struggle to raise children in happy homes which makes these children more prone to crime.
The African American poor communities in the US is a good example of these issues.
Although, some DC countries like Australia have quite a low crime rate, so this may not be a direct result of DC.
There are factors that can push people towards crime in DC, but socialist versions of DC do not particularly have an issue with this.