Parkinson's disease (PD) has broadly been associated with mild cognitive impairment (PDMCI) and dementia (PDD). Researchers have studied surrogate, neuroanatomic biomarkers provided by magnetic resonance imaging (MRI) that may help in the early diagnosis of this condition. In this article, four classification models (naïve Bayes, multivariate filter-based naïve Bayes, filter selective naïve Bayes and support vector machines, SVM) have been applied to evaluate their capacity to discriminate between cognitively intact patients with Parkinson's disease (PDCI), PDMCI and PDD. For this purpose, the MRI studies of 45 subjects (16 PDCI, 15 PDMCI and 14 PDD) were acquired and post-processed with Freesurfer, obtaining 112 variables (volumes of subcortical structures and thickness of cortical parcels) per subject. A multivariate filter-based naïve Bayes model was found to be the best classifier, having the highest cross-validated sensitivity, specificity and accuracy. Additionally, the most relevant variables related to dementia in PD, as predicted by our classifiers, were cerebral white matter, and volumes of the lateral ventricles and hippocampi.