A high resolution small animal PET scanner that employs Silicon Photomultiplier (SiPM) matrices as photodetectors is under development at the University of Pisa and INFN Pisa. The first SiPM matrices fabricated by the Center for Scientific and Technological Research, FBK-irst (Trento, Italy), are being evaluated for this purpose. The devices are composed of 16 (4 times4) pixel elements of 1 mmtimes1 mm in a common substrate. The first tests have been carried out employing the ASIC MAROC2 for the readout. Energy and timing resolution, and position determination tests have been performed coupling both pixellated and continuous LYSO scintillator crystals to the matrix, and the results have been compared with the ones obtained for single SiPMs. The first tests on position determination with continuous crystals and SiPM matrices have been performed. An intrinsic spatial resolution of 0.61 mm FWHM has been obtained.