The master stability function is a powerful tool for determining synchrony in high dimensional networks of coupled limit cycle oscillators. In part this approach relies on the analysis of a low dimensional variational equation around a periodic orbit. For smooth dynamical systems this orbit is not generically available in closed form. However, many models in physics, engineering, and biology admit to piece-wise linear (pwl) caricatures which are also often nonsmooth, for which it is possible to construct periodic orbits without recourse to numerical evolution of trajectories. A classic example is the McKean model of an excitable system that has been extensively studied in the mathematical neuroscience community. Understandably the master stability function cannot be immediately applied to networks of such elements if they are non-smooth. Here we show how to extend the master stability function to nonsmooth planar pwl systems, and in the process demonstrate that considerable insight into network dynamics can be obtained when choosing the dynamics of the nodes to be pwl. In illustration we highlight an inverse period-doubling route to synchrony, under variation in coupling strength, in linearly coupled networks for which the node dynamics is poised near a homoclinic bifurcation. We contrast this with node dynamics poised near a non-smooth Andronov-Hopf bifurcation and also a saddle node bifurcation of limit cycles, for which no such bifurcation of synchrony occurs.