In this paper we describe the overall design of a PET–MR system for head imaging within the framework of the DREAM Project as well as the first detector module tests. The PET system design consists of 4 rings of 16 detector modules each and it is expected to be integrated in a head dedicated radio frequency coil of an MR scanner. The PET modules are based on monolithic LYSO crystals coupled by means of optical devices to an array of 256 Silicon Photomultipliers. These types of crystals allow to preserve the scintillation light distribution and, thus, to recover the exact photon impact position with the proper characterization of such a distribution. Every module contains 4 Application Specific Integrated Circuits (ASICs) which return detailed information of several light statistical momenta. The preliminary tests carried out on this design and controlled by means of ASICs have shown promising results towards the suitability of hybrid PET–MR systems.