Dissociation of the 2s (2)A(1)’, 2p (2)A(2) ", 3s (2)E " and 3d (2)E " Rydberg states of the H-3 molecule is investigated using a fast neutral beam photofragment spectrometer. A beam of 3-6 keV metastable H-3 2p (2)A(2) " (N=K=0) molecules, generated by charge transfer neutralization of H-3(+) ions in Cs vapor, is intersected by a laser beam to selectively populate a specific rovibrational level in each of the H-3 states for study. The correlated pair of fragments H+H-2, created by dissociation of the H-3 state, is observed by a time- and position-sensitive detector, which specifies the fragments’ center-of-mass kinetic energy release and angle of ejection. The 3s (2)A(1)’ (N=1, K=0) and 3d (2)E " 1 (N=1, G=0, R=1) rotational levels are prepared either in their ground vibrational states or in vibrationally excited states by pumping transitions from the 2p (2)A(2) " (N=K=0) level with a tunable dye laser. All of these photoexcited levels are observed to both predissociate and to radiate into the dissociative ground state. In contrast, the 2s (2)A(1)’(N=1, K=0) level, produced by stimulated emission pumping from the 2p (2)A(2) " (N=K=0) level using a CO2 laser, is observed to only predissociate. Predissociation of the H-3 produces a discrete release of kinetic energy to the H+H-2 fragments that uniquely identifies the production of a specific rovibrational level in the H-2. Monte Carlo simulation of the detector response, combined with observation of the corresponding dissociations in D-3 (where predissociation is essentially negligible), allows quantitative separation of H+H-2 predissociation fragments from a background of continuous energy release produced by radiative dissociation. Branching ratios in the radiative and the predissociative decay channels are estimated and detailed distributions for the production of the H-2(v,J) final state are determined. Comparison of experimental distributions with recent theoretical calculations illuminates the important role nonlinear couplings play in determining the dissociation dynamics of a particular H-3 Rydberg state. Additionally, transition energies for the vibrationally excited levels of H-3 are determined with improved accuracy, the relative importance of the H+H+H dissociation channel is estimated, and spontaneous dissociation of the metastable 2p (2)A(2) " (N=K=0) level is discussed.