  Let $\mathscr{F}=(M,\mathscr{L},E)$ be a Brody-hyperbolic singular
holomorphic foliation on a compact complex manifold $M$. Suppose that
$\mathscr{F}$ has isolated singularities and that its Poincar\'e metric is
complete. This is the case for a very large class of singularities, namely,
non-degenerate and saddle-nodes in dimension $2$. Let $\mu$ be an ergodic
harmonic measure on $\mathscr{F}$. We show that the upper and lower local
hyperbolic entropies of $\mu$ are leafwise constant almost everywhere.
Moreover, we show that the entropy of $\mu$ is at least $2$.
