With the newly available data sets on hadronic tau decays from the B-factories BaBar and BELLE, and future data from BESIII, precise information on the decay distributions will soon become available. This calls for an improvement of the decay spectra also on the theoretical side. In this work, the distribution function for the decay tau -> v(tau)K pi will be presented with the relevant K pi vector and scalar forth factors being calculated in the framework of the resonance chiral theory, also taking into account additional constraints from dispersion relations and short-distances. As a by-product the slope and curvature of the vector form factor F-+(K pi)(s) are determined to be lambda'(+) = 25.6 x 10(-3) and lambda'(+) = 1.31 x 10(-3) respectively. From our approach it appears that it should be possible to obtain information on the low lying scalar K*(800) as well as the sec0 ond vector K*(1410) resonances from the tau decay data. In particular, the exclusive branching fraction of the scalar component is found to be B[tau -> vT (K pi)(S-wave)] = (3.88 +/- 0.19) x 10(-4).