[wrycoder]

It is presumed that the dark matter also rotates about the galactic center. It can’t fall in, any more than the stars in the galaxy can, because it collectively can’t dump its angular momentum. However, there is controversy whether dark matter can dissipate momentum that is parallel to the rotational axis either by self interaction or by interaction with ordinary matter. If it can, then the distribution of dark matter could resemble a disk, as opposed to a spherical distribution.

Lisa Randall has written a provocative book about this which will answer your question in depth: Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe.