According to AS 9 Pro documentation, the supported movie types are AVI and QuickTime.
***** From AS 9.0 Manual (Import Chapter) *******
Movie: Imports a movie file as a new Image layer. Anime Studio supports importing QuickTime (Windows and Mac OS) and AVI (Windows only) movie files. A movie that you import into Anime Studio will play back along with the Anime Studio animation, allowing you to combine 2D and 3D elements, or to composite an Anime Studio animation on top of a pre-recorded video sequence.On Windows, if you have problems importing QuickTime movies, then you probably need to download and install QuickTime.
However I have the same problem even with an AVI which I exported from Anime Studio in the first place. It imports but just shows the broken image icon and doesn't play back. Would be interested if anyone has successfully imported an AVI.