  This paper studies the existence of non trivial $\mu_p$ actions on a
canonically polarized surface X defined over an algebraically closed field of
characteristic p>0. In particular, an explicit function $f(K_X^2)$ is obtained
such that if $p>f(K_X^2)$, then there does not exist a non trivial
$\mu_p$-action on X. This implies that the connected component of the
automorphism scheme of X containing the identity is either smooth or is
obtained by successive extensions by $\alpha_p$.
