We investigate the velocity distribution of dark matter in the disk of a galaxy like the Milky Way at the solar radius. Using N-body simulations with the total mass and z-component of angular momentum conserved, we calculate the response of a dissipationless dark matter galactic halo during the dissipational collapse of the baryonic matter in spiral galaxy formation. The initial distribution of dark matter and baryonic particles is assumed to be a homogeneous mixture based on a King model. The baryonic matter is assumed to contract, forming the final luminous components of the galaxy, namely the disk and, in some cases, a bulge and central point. Both slow and fast growth of the luminous components are considered. We find that the velocity distribution of dark matter particles in a reference frame rotating slowly about the galaxy center in the plane of the disk is similar to a Maxwellian, but it is somewhat boxier, being flatter at the peak and truncated in the tails of the distribution. We tabulate parameters for the best-fitting Maxwellian and modified-Maxwellian distributions. There is no significant difference between slow collapse and fast collapse for all these results. We were unable to detect any effect of disk formation on the z-dependence of the dark matter density distribution.