We address the problem of farm and parasitic risk profiling in the context of Veterinary Epidemiology. We take advantage of a cross-sectional study carried out in the Campania Region in order to study the spatial distribution of 16 parasites in 121 ovine farms. We propose a tri-level hierarchical Bayesian model, which account for multivariate spatially structured overdispersion, to obtain estimate of posterior classification probabilities, that is for each parasite and farm the probability to belong to the set of the null hypothesis. We explore four decision rules based on either posterior probabilities or posterior means and compare the results in terms of the number of false discoveries/non-discoveries or the rate of false discovery/non-discovery. Our approach proved useful for parasitological risk profiling and we show that decision rules can be easily handled.