Haptic perception of softness is a unique feature of the human skin that relies on the concurrent measurements of the lateral deformation and compression of the skin during object manipulation. This is challenging to implement in robotics because of combined requirements in sensing modalities, skin format, robotic structures, and synthetic materials. A soft sensory skin supporting distributed and bimodal mechanical sensing over large surface area and suitable for robotic hand manipulation is reported. Resistive pressure and strain sensors are prepared with spray-coated liquid metal films embedded in a silicone matrix. Object softness is computed through a calibrated model based on both sensor response curves and the stiffness of the carrier robot. The soft sensory skin enables localization and discrimination of softness that promise interesting future implementation for robotic palpation or precise teleoperation.