The mutual information (MI) of multiple-input multiple-output (MIMO) system over Rayleigh fading channel is known to asymptotically follow a normal probability distribution. In this paper, we first prove that the MI of distributed MIMO (DMIMO) system is also asymptotically equivalent to a Gaussian random variable (RV) by deriving its moment generating function (MGF) and by showing its equivalence with the MGF of a Gaussian RV. We then derive an accurate closed-form approximation of the outage probability for DMIMO system by using the mean and variance of the MI and show the uniqueness of its formulation. Finally, several applications for our analysis are presented.