The photofragment imaging technique is used to measure the velocity distributions of the Br(2P3/2) and Br*(2P1/2) atoms formed following laser dissociation of CH3Br and CD3Br at 205 nm. The speed and angular distributions are markedly different for the two bromine electronic states. The Br* images are anisotropic and have the appearance of a cos2-theta angular distribution indicative of a parallel transition. The Br ground-state images appear more isotropic but contain a distinct sin2-theta angular component. The speed distributions extracted from the Br* images are narrow compared with the Br speed distributions. This indicates that the sibling methyl fragments formed in the Br dissociation channel have greater internal excitation than the methyl fragments formed in the Br* dissociation channel. The results are compared with methyl iodide dissociation and the importance of surface crossings in the dissociation is discussed.