Human-robot collision has drawn increasing attention in recent years and collision safety can be improved by successfully detecting collisions between a human and a robot. For a manipulator working in human environments, collisions usually occur at the manipulator body while the robot performs a contact task using its end-effector to interact with the environment. Therefore, both collision force and the force on the end-effector contribute to the external torques which can be estimated from the robot dynamics and the joint torques measured by the joint torque sensors, which means whether or not a collision has occurred cannot be reliably determined using this estimation. In this study, we propose a novel collision detection index to detect collisions independently of the end-effector force of a redundant manipulator equipped with joint torque sensors. Using the null space projection of a redundant manipulator, the collision detection index can be expressed as a function of the torque generated by a collision and the manipulator configuration. The proposed index is verified through various simulations. Simulation results show that collisions can be reliably detected regardless of the presence of the end-effector forces even in situations with external torques contaminated by substantial error.