We report state-to-state cross sections and thermal rate constants for vibrational and rotational relaxation of OH((2)Pi) by collision with H atoms. The cross sections are calculated by the coupled-states (CS) statistical method including the full open-shell character of the OH + H system. Four potential energy surfaces (PESs) ((1.3)A' and (1.3)A") describe the interaction of OH(X-2 Pi) with H atoms. Of these, three are repulsive, and one (W) correlates with the deep H2O well. Consequently, rotationally and ro-vibrationally inelastic scattering of OH in collisions with H can occur by scattering on the repulsive PESs, in a manner similar to the inelastic scattering of OH by noble gas atoms, or by collisions which enter the H2O well and then reemerge. At 300 K, we predict large (approximate to 1 x 10(-10) cm(3) molecule(-1) s(-1)) vibrational relaxation rates out of both nu = 2 and nu = 1, comparable to earlier experimental observations. This anomalously fast relaxation results from capture into the H2O complex. There exists a significant propensity toward formation of OH in the Pi(A') A-doublet level. We also report state-resolved cross sections and rate constants for rotational excitation within the OH nu = 0 manifold. Collisional excitation from the F-1 to the F-2 spin-orbit manifold leads to an inverted A-doublet population.