  Motivated by the anomalous c-axis transport properties of the quasi
two-dimensional metal, $\rm Sr_2 Ru O_4$, and related compounds, we have
studied the interlayer hopping of single electrons that are coupled strongly to
c-axis bosons. We find a c-axis resistivity that reflects the in-plane
electronic scattering in the low and very high temperature limits (relative to
the characteristic temperature of the boson $T_{\rm boson}$). For temperatures
near the $T_{\rm boson}$, a broad maximum in the resistivity can appear for
sufficiently strong electron-boson coupling. This feature may account for the
observed ``metallic to non-metallic crossover'' seen in these layered oxides,
where the boson may be a phonon.
