The first prototype of the Schwarzschild Couder Medium Size Telescope (pSCT) proposed for the CTA observatory has been installed in 2018 at the Fred Lawrence Whipple Observatory. The pSCT camera is composed of 25 modules with 64 channels each, covering only a small portion of the full focal plane of the telescope. The Italian Institute of Nuclear Physics (INFN) has developed and characterized in collaboration with Fondazione Bruno Kessler (FBK) a new generation of Silicon Photomultipliers (SiPMs) sensitive to the Near Ultraviolet wavelengths, based on the High Density technology (NUV-HD devices). The latest generation of 6×6 mm2 SiPMs (called NUV-HD3) have been used to equip a subsection of 9 out of 25 modules of the pSCT camera. An upgrade of this camera is foreseen between 2019 and 2020 using the same sensors, aiming to equip the full focal plane with 177 modules, for a total of more than 11000 pixels. We will present a full characterization of the performance of these devices, highlighting why they are suitable for Cherenkov light detection. An overview on the overall behavior of the installed sensors will be also given, providing information on the uniformity of the sensors and of the performance of the camera.