The results of study of electron emission and capture processes for an amphoteric (having a donor and an acceptor levels) hydrogen-related center with negative-U properties in crystalline silicon are presented. It is found that only singly negatively and singly positively charged states of the defect are stable, but for the description of the transient process between these states thermodynamically unstable neutral charge state should be taken into account. Two local energy minima in configurational space are suggested to be present for this state. A non-equilibrium occupancy statistics for the negative-U centers with such an electronic structure has been developed and analytical expression for the time constant of the occupancy transient process (τf) is obtained. Experimentally observed τf-1(1/T) dependencies were described perfectly by applying the developed statistics and the values of energy barriers for the electron capture and emission were determined.