Because I wanted to focus on somewhere outside the US, I decided to do a scatterplot of suicide and homicide in the EU.
I have heard a theory that suicide and homicide are inverse expressions of the same feeling, and that in different cultures, violence is taken out differently, as is considered appropriate. But what does the data say? The bad, bad data. This is the most fragmented data I have looked at so far (off of wikipedia tables), even ignoring for the fact that depending on the country, reporting of homicides AND suicides might be a little suspect. But enough explanation:
There doesn't seem to be any inverse correlation between the two, quite the contrary, with this data, violence against self and others is correlated, although much of that has to do with three significant outliers, the Baltic Republics. Without those, there wouldn't be much correlation at all.