Prostate Cancer (PCa) is the most common oncological disease in Western men. Even though a growing effort has been carried out by the scientific community in recent years, accurate and reliable automated PCa detection methods on multiparametric Magnetic Resonance Imaging (mpMRI) are still a compelling issue. In this work, a Deep Neural Network architecture is developed for the task of classifying clinically significant PCa on non-contrast-enhanced MR images. In particular, we propose the use of Conditional Random Fields as a Recurrent Neural Network (CRF-RNN) to enhance the classification performance of XmasNet, a Convolutional Neural Network (CNN) architecture specifically tailored to the PROSTATEx17 Challenge. The devised approach builds a hybrid end-to-end trainable network, CRF-XmasNet, composed of an initial CNN component performing feature extraction and a CRF-based probabilistic graphical model component for structured prediction, without the need for two separate training procedures. Experimental results show the suitability of this method in terms of classification accuracy and training time, even though the high-variability of the observed results must be reduced before transferring the resulting architecture to a clinical environment. Interestingly, the use of CRFs as a separate postprocessing method achieves significantly lower performance with respect to the proposed hybrid end-to-end approach. The proposed hybrid end-to-end CRF-RNN approach yields excellent peak performance for all the CNN architectures taken into account, but it shows a high-variability, thus requiring future investigation on the integration of CRFs into a CNN.