We performed a theoretical study of the photodissociation dynamics of CH(3)Br in the A band using a wave packet propagation technique on coupled ab initio potential energy curves. The present model involves the (3)Q(1) and (1)Q(1) excited states which can be populated from the ground state by a perpendicular transition and which are correlated at large methyl-bromide distance to the ground bromide spin-orbit state, as well as the (3)Q(0) and 4E states which can be excited by a parallel and perpendicular transition (respectively) and both correlate to excited Br(*) spin-orbit state. The model provides absorption cross sections and branching ratios in excellent agreement with experimental results. Due to weak spin-orbit interaction, the (1)Q(1) state is the dominant contributor to the absorption cross section, except for the red wing of the band where (3)Q(0) and (3)Q(1) states have significant absorption. However, spin-orbit coupling is strong enough to induce nonadiabatic transitions between the (3)Q(1) and (1)Q(1) states during the dissociation process which should be experimentally detectable in the alignment properties of the fragments. Nonadiabatic transitions at the conical intersection between (3)Q(0) and (1)Q(1) are shown to play a minor role in this system.