We study the asymptotic properties of a diffusion process associated to a pure non-divergence second order operator with stationary and ergodic coefficients. We first remind the reader of the ergodic properties of the so-called environment seen from the particle and then investigate the underlying rate of convergence. We establish more specifically a central limit theorem for additive functionals driven by suitable stationary fields. Our analysis relies on earlier results for adjoint solutions to second order non-divergence elliptic and parabolic equations.