  We report on a search for the parental molecular clouds of the TW Hya
association (TWA), using CO emission and Na I absorption lines. TWA is the
nearest young (~ 50 pc; ~ 10 Myr) stellar association, yet in spite of its
youth, there are no detection of any associated natal molecular gas, as is the
case for other typical young clusters. Using infrared maps as a guide, we
conducted a CO cloud survey toward a region with a dust extinction of E(B-V) >
0.2 mag, or AV > 0.6 mag. CO emission is detected toward three IR dust clouds,
and we reject one cloud from the TWA, as no interstellar Na absorption was
detected from the nearby Hipparcos stars, implying that it is too distant to be
related. The other two clouds exhibit only faint and small-scale CO emission.
Interstellar Na I absorptions of Hipparcos targets, HIP 57809, HIP 64837, and
HIP 64925 (at distances of 133, 81, and 101 pc, respectively) by these couds is
also detected. We conclude that only a small fraction of the interstellar
matter (ISM) toward the IR dust cloud is located at distance less than 100 pc,
which may be all that is left of the remnant clouds of TWA; the remaining
remnant cloud having dissipated in the last ~ 1 Myr. Such a short dissipation
timescale may be due to an external perturbation or kinematic segregation that
has a large stellar proper motion relative to the natal cloud.
