We have investigated the timing performance of P-on-N and N-on-P silicon photomultipliers (SiPM) in light of their use in time-of-flight (TOF) positron emission tomography (PET) detectors. Polished 3 mm × 3 mm × 5 mm and 3 mm × 3 mm × 20 mm LYSO:Ce scintillators were coupled to STmicroelectronics P-on-N and N-on-P SiPMs. The SiPMs were read out with low-noise RF transimpedance amplifiers and fed to a waveform digitizer for offline time pickoff analysis. For the P-on-N devices coincidence resolving times (CRTs) of 234 ps and 189 ps FWHM were obtained with the 3 mm × 3 mm × 20 mm and 3 mm × 3 mm × 5 mm crystals, respectively. For the N-on-P devices CRTs of 280 ps and 214 ps FWHM, respectively, were obtained with above crystal types. The P-on-N devices are promising for TOF-PET due to their high photon detection efficiency (PDE) and low transit time spread (TTS).