In this old research study (Perceptual And Motor Skills. 1976. Dec; Vol. 43, pp. 843-7), 1,154 pairs of high school students were observed in cafeteria queues. Blacks were found to touch others more frequently than whites. This is consistent with Francis Galton's claim that Africans are affectionate and gregarious. Over the years, my observation has been that blacks are more extraverted, but self-assessment data (GSS) don't back me up.
Behavioral studies, like this one on touching, seem to offer a more valid way to identify personality differences between races. One interesting approach is to study the items in people's offices or homes, as is described in Snoop: What Your Stuff Says about You.
I can't call it a study, but I have gotten an impression of racial differences from behavior in the classroom. If I measure extraversion as the frequency of speaking up in class--or perhaps approaching me with questions--blacks are the most extraverted, whites are in the middle, and Mex-Ams are the most introverted.
If I measure conscientiousness in terms of the how perfectionistic students are when writing their papers, whites would score the highest, Mex-Ams in the middle, and blacks would come in last. Or if I measured the trait by punctuality and attendance, the racial order would be the same.
If I measure disagreeableness in terms of students arguing with me, blacks rank first, whites second, and Mex-Ams third.
It's not as easy to measure neuroticism, but based on expressing emotional difficulties to me, whites do it the most. Hispanics are less likely to talk to me, period. Blacks talk to me plenty, but are more likely to talk about problems in terms of circumstances, not feelings.