We investigate the relations between the $K_{l3\mathrm{}}$ and $\overrightarrow{\tau }K\pi {\nu }_{\tau }$ decays using the meson dominance approach. First, the experimental branching fractions (BF) for $K_{e3\mathrm{}}^{\pm }$ and $K_{e3\mathrm{}}^0$ are used to fix two normalization constants (isospin invariance is not assumed). Then, the BF of ${\tau }^{-}\to K^{*}{\mathrm{}\left(892\right)\mathrm{}}^{-}{\nu }_{\tau }$ is calculated in agreement with experiment. We further argue that the nonzero value of the slope parameter ${\lambda }_0$ of the $K_{\mu 3}^{\pm }$ and $K_{\mu 3}^0$ form factors $f_0\mathrm{}\left(t\right)\mathrm{}$ implies the existence of the ${\tau }^{-}\to K_0^{*}{\mathrm{}\left(1430\right)\mathrm{}}^{-}{\nu }_{\tau }$ decay. We calculate its BF, together with the BF’s of the $K_{\mu 3}^{\pm },$ $K_{\mu 3}^0,$ ${\tau }^{-}\to K^{-}{\pi }^0{\nu }_{\tau },$ and ${\tau }^{-}\to K^0{\pi }^{-}{\nu }_{\tau }$ decays, as a function of the ${\lambda }_0$ parameter. At some value of ${\lambda }_0,$ different for charged and neutral kaons, the calculated BF’s seem to match existing data and a prediction is obtained for the $\overrightarrow{\tau }K\pi \nu$ decays going through the $K_0^{*}{\mathrm{}\left(1430\right)\mathrm{}}^{-}$ resonance.

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