Silenced Pistol is characterized by low damage in comparison with the abovementioned shotgun but the attached silencer lets you efficiently eliminate human enemies without the risk of alarming everyone nearby.
Silenced Pistol can be found in Teleconferencing, an area found on the third floor of Talos I Lobby. Once you're close to the area, defeat a group of Mimics guarding the center. The pistol should be lying on the floor (screenshot above)
The weapon can also appear randomly in different areas found in game, for example in Morgan's office found on the third floor of the lobby.