A general theory is developed for the angular distribution of Auger electrons emitted in the decay of molecular vacancies created by electron impact. The molecules are assumed as freely rotating. General expressions are derived where the angular distribution of the emitted Auger electrons is related to the anisotropy of the molecular axis distribution and to the shape and spatial orientation of the electronic orbitals prior to the Auger emission. Particular emphasis is placed on the correct formulation of the coherences produced during the ionization which requires an extension of previously derived formulas. The obtained equations are a necessary first step for future numerical calculations.