We have carried out (CO)-C-12 J = 2-1 line observations of the supernova re
mnant (SNR) HE 21 in order to search for evidence of interaction with molec
ular clouds. We mapped the eastern half (80' x 110') of the SNR almost comp
letely. Molecular gas appears to be distributed mainly along the boundary o
f the SNR, but the overall distribution has little correlation either with
the distortion of the SNR boundary or with the distribution of radio bright
ness. Along the eastern boundary, where the SNR was considered to be intera
cting with molecular clouds in previous studies, we have not found any stro
ng evidence for the interaction. Instead, we detected broad (20-40 km s(-1)
) CO emission lines in the northern and southern parts of the SNR. In the n
orthern area, the broad-line emitting cloud is composed of a small (similar
to2' or 0.5 pc), very bright, U-shaped part and several clumps scattered a
round it. There is a significant enhancement of radio emission with a flat
(-0.28 +/- 0.17) spectral index possibly associated with this cloud. In the
southern area, the broad-line emitting cloud is filamentary and appears to
form an elongated loop of similar to 30' in extent. Small (less than or si
milar to 1.'2 or 0.3 pc), bright clumps are seen along the filamentary stru
cture. We have obtained sensitive J = 1-0 and J = 2-1 spectra of (CO)-C-12
and (CO)-C-13 molecules toward several peak positions. The intensity of (CO
)-C-12 J = 2-1 emission is low (T-mb < 7 K) and the ratio of (CO)-C-12 J =
2-1 to J = 1-0 integrated intensities is high (1.6-2.3), which suggests tha
t the emission is from warm, dense, and clumpy gas. We have applied a large
velocity gradient analysis to derive their physical parameters. The detect
ed broad CO lines are believed to be emitted from the fast-moving molecular
gas swept up by the SNR shock. The small (<less than or similar to>20 km s
(-1)) shock velocity suggests that the shock is a nondissociating C-shock.
We discuss the correlation of the shocked molecular gas with the previously
detected, shocked atomic gas and the associated infrared emission.