  In this paper, we are concerned with centered Markov Additive Processes
$\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$
has a finite state space. Under suitable conditions, we provide a local limit
theorem for the density of the absolutely continuous part of the probability
distribution of $t^{-1/2}Y_t$ given $X_0$. The rate of convergence and the
moment condition are the expected ones with respect to the i.i.d case. An
application to the joint distribution of local times of a finite jump process
is sketched.
