Yes, there is a large correlation.
There is nothing special about the race. The same correlation will be found for any characteristic that tends to represent the circle of family and friends.
While crime study isn't hard science, there's little doubt that people are more likely to commit crimes if they grow up in dysfunctional families or are surrounded by peers disaffected by the society.
So, for example, the crime rates among the whites are highly correlated to whether their older relatives or their neighbors or classmates were involved in crimes.
As we know, despite the many decades of efforts, our society has not yet fixed the huge inequality in how different people are brought up. Therefore, the correlation between race and crime will likely persist until ever person, regardless of their community, skin color, or income level, has high quality childhood experience brought by good role models inside and outside of home.