The theory of the dynamic plasma response in laser-photodetachment experiments in low pressure hydrogen plasmas is extended to include the effects of the self-consistent electric field. The H[sup [minus]] rich plasma is modeled via a hybrid fluid-kinetic approach in which the electrons and positive ions are described by the fluid theory, while the negative ions are treated within the ballistic kinetic theory. Both slab and cylindrical geometries of the plasma region illuminated by the laser are analyzed. The model is applied for studying the space-time evolution of various plasma species after the photodetaching laser pulse. The experimentally observed overshoot in the time dependence of the electron density perturbation on the axis or plane of symmetry was analyzed in detail. The overshoot is due to the depletion of the positive ions as the result of the self-consistent electric field. The magnitude of the overshoot and the time of the maximum depletion of the positive ions are sensitive to the ratio between the electron and positive ion temperatures.