Dental research gives rise to data with potentially complex correlation structure. Assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject's mouth. In addition to this nesting, caries outcome exhibit spatial structure among neighboring teeth. We develop a Bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth. Using a sample from a clinical study conducted at the Medical University of South Carolina, we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience.