As it happens, despite yet unmatched by robots perception and motor skills humans drop objects during handover because of false grasp detection and early release. Accordingly, the fluent robot-human handover is still an open challenge. This paper presents an approach to a natural robot to human handover using Capacitive Proximity Sensor (CPS) for robust grasp detection and release trigger. We propose an experimental setup for the evaluation using a collaborative robot, an eye-in-hand depth camera, and CPS integrated into the gripper. Three grasp detection methods were implemented and an object release was triggered based on torque-sensing, capacitive sensing, and the combination of both. Finally, a user study was designed and conducted, indicating that the capacitive method is the most preferred type with the shortest human idle time and the highest fluency ratings.