In this work, we investigate some major issues for the use of silicon photomultiplier (SiPM) devices in continuous wave functional near-infrared spectroscopy (CW fNIRS). We analyzed the after-pulsing effect, proposing the physical mechanism causing it, and determining its relevance for CW fNIRS. We studied the SiPM transients occurring as the SiPM device goes from the dark (LED in off state) to the illumination (LED in on state) conditions, and vice-versa. Finally, we studied the SiPM SNR in standard CW fNIRS operation.