We identified 46 unresolved source candidates in the Hubble Ultra Deep Field, down to i775 = 29.5. Unresolved objects were identified using a parameter S, which measures the deviation from the curve-of-growth of a point source. Extensive testing of this parameter was carried out, including the effects of decreasing signal-to-noise and of the apparent motions of stars, which demonstrated that stars brighter than i775 = 27.0 could be robustly identified. Low resolution grism spectra of the 28 objects brighter than i775 = 27.0 identify 18 M and later stellar type dwarfs, 2 candidate L-dwarfs, 2 QSOs, and 4 white dwarfs. Using the observed population of dwarfs with spectral type M4 or later, we derive a Galactic disk scale height of 400 \pm 100 pc for M and L stars. The local white dwarf density is computed to be as high as (1.1 \pm 0.3) x10^(-2) stars/pc^3. Based on observations taken 73 days apart, we determined that no object in the field has a proper motion larger than 0.027"/year (3 sigma detection limit). No high velocity white dwarfs were identified in the HUDF, and all four candidates appear more likely to be part of the Galactic thick disk. The lack of detected halo white dwarfs implies that, if the dark matter halo is 12 Gyr old, white dwarfs account for less than 10% of the dark matter halo mass.

35 pages, 11 figures, accepted by ApJ