  In planar analytic vector fields, a monodromic singularity can be
distinguished between a focus or a center by means of the Lyapunov
coefficients, which are given in terms of the power series coefficients of the
first-return map defined around the singularity. In this paper, we are
interested in an analogous problem for monodromic tangential singularities of
piecewise analytic vector fields $Z=(Z^+ ,Z^-)$. First, we prove that the
first-return map, defined in a neighborhood of a monodromic tangential
singularity, is analytic, which allows the definition of the Lyapunov
coefficients. Then, as a consequence of a general property for pair of
involutions, we obtain that the index of the first non-vanishing Lyapunov
coefficient is always even. In addition, a general recursive formula together
with a Mathematica algorithm for computing the Lyapunov coefficients is
obtained. We also provide results regarding limit cycles bifurcating from
monodromic tangential singularities. Several examples are analyzed.
