Approximations of the distribution for the maximum likelihood estimator of the dispersion matrix in the Growth Curve model due to Potthoff and Roy 0964) are considered. Three different approaches are presented. Two are based on an Edgeworth type expansion where as approximating distribution two different Wishart distributions are used. In a third approach we utilize the structure of the estimator and combine an Edgeworth type expansion with an approach put forward by Fujikoshi (1985).