Let $\cal V$ be a complete connected hyperbolic 3-manifoldof finite volume, with Liouville measure $m$, geodesic flow$\Gamma_t$ and Brownian motion $Z_t$. Let $\omega$ be a smooth 1-form, closed in the cusps of $\cal V$. Then the limit laws as $t \to \infty$ of $(t\log t)^{-1/2}\int_0^t\omega(\Gamma_s)$ under$m$ and of $(t\log t)^{-1/2}\int_0^t\omega(Z_s)$are calculated, and seen to be Gaussian, and equal. Thegeodesic flow case is studied via the Brownian case.

1991 Mathematics Subject Classification: 60J65, 58F17, 51M10.