We present Ha narrow-band imaging of 17 dwarf irregular (dI) galaxies in the nearby Centaurus A Group. Although all large galaxies of the group are or recently have been through a period of enhanced star formation, the dIs have normal star formation rates (SFRs) and do not contain a larger fraction of dwarf starbursts than other nearby groups such as the Sculptor Group or the Local Group. Most of the galaxies in the group now have fairly accurately known distances, which enables us to obtain relative distances between dIs and larger galaxies of the group. We find that the dI SFRs do not depend on local environment, and in particular they do not show any correlation with the distance of the dI to the nearest large galaxy of the group. There is a clear morphology-density relation in the Centaurus A Group, similar to the Sculptor Group and Local Group, in the sense that dwarf ellipticals (dEs)/dwarf spheroidals (dSphs) tend to be at small distances from the more massive galaxies of the group, while dIs are on average at larger distances. We find four transition dwarfs in the Group, dwarfs that show characteristics of both dE/dSphs and dIs, and which contain cold gas but no current star formation. Interestingly, the transition dwarfs have an average distance to the more massive galaxies, which is intermediate between those of the dEs/dSphs and dIs and which is quite large: 0.54 +/- 0.31 Mpc. This large distance poses some difficulty for the most popular scenarios proposed for transforming a dI into a dE/dSph (ram-pressure with tidal stripping or galaxy harassment). If the observed transition dwarfs are indeed missing links between dIs and dE/dSphs, their relative isolation makes it less likely to have been produced by these mechanisms. An inhomogeneous intergalactic medium containing higher density clumps would be able to ram-pressure strip the dIs at larger distances from the more massive galaxies of the group.