The paper is motivated by a problem in veterinary epidemiology, in which spatially referenced breakdowns of bovine tuberculosis are classified according to their genotype and year of occurrence. We develop a nonparametric method for addressing spatial segregation in the resulting multivariate spatial point process, with associated Monte Carlo tests for the null hypothesis that different genotypes are randomly intermingled and no temporal changes in spatial segregation. Our spatial segregation estimates use a kernel regression method with bandwidth selected by a multivariate cross-validated likelihood criterion.