  We present high-resolution echelle observations of SN 2011dh, which exploded
in the nearby, nearly face-on spiral galaxy M51. Our data, acquired on three
nights when the supernova was near maximum brightness, reveal multiple
absorption components in Na I D and Ca II H and K, which we identify with
gaseous material in the Galactic disk or low halo and in the disk and halo of
M51. The M51 components span a velocity range of over 140 km s^-1, extending
well beyond the range exhibited by H I 21 cm emission at the position of the
supernova. Since none of the prominent Na I or Ca II components appear to
coincide with the peak in H I emission, the supernova may lie just in front of
the bulk of the H I disk. The Na I/Ca II ratios for the components with the
most extreme positive and negative velocities relative to the disk are ~1.0,
similar to those for more quiescent components, suggesting that the absorption
originates in relatively cool gas. Production scenarios involving a galactic
fountain and/or tidal interactions between M51 and its companion would be
consistent with these results. The overall weakness of Na I D absorption in the
direction of SN 2011dh confirms a low foreground and host galaxy extinction for
the supernova.
