An ab initio configuration interaction (CI) study including the spin-orbit interaction is carried out for numerous valence and Rydberg states of the AsH radical by employing a relativistic effective core potential for the arsenic atom. The computed spectroscopic constants are in good agreement with corresponding experimental data, with a tendency toward a slight overestimation of bond lengths (by 0.01-0.02 Angstrom) and T-e values (by 450-550 cm(-1)) for the lowest singlet states. Measured spin-orbit splittings for the X (3) Sigma(-) and A (3) Pi multiplets are also accurately reproduced in the present calculations and the Omega = 0(-), 1, and 2 components of the latter state are shown to be strongly predissociated due to spin-orbit interaction with the corresponding components of the repulsive (5) Sigma(-) state. Dipole moments mu(upsilon = 0) for the lowest-lying X (3) Sigma(-), a (1) Delta, and b (1) Sigma(+) states, all arising from the ...sigma(2) pi(2) electronic configuration, are computed to have small (e.g., 0.1266 D for X-1 (3) Sigma(0+)(-)) and nearly equal positive values (As-H+ polarity). This finding is used to explain why the partial radiative lifetime for the parallel b-X-1 transition (tau(p) = 44 ms) is much longer than that (tau(p) = 0.95 ms) of the perpendicular b-X-2. The lifetime of the a (1) Delta state is calculated to be 97 ms, significantly longer than that of the b (1) Sigma(+) state, while the A (3) Pi substates have much shorter lifetimes (less than or equal to 1 mu s) for radiative decay to the X (3) Sigma(-) ground state. A number of other bound states and avoided crossings are indicated in the calculations which may be of relevance in future experimental studies of this system.