We have carried out ^ { 12 } CO J=2–1 line observations of the supernova remnant ( SNR ) HB 21 in order to search for evidence of interaction with molecular clouds . We mapped the eastern half ( 80 ^ { \prime } \times 110 ^ { \prime } ) of the SNR almost completely . Molecular gas appears to be distributed mainly along the boundary of the SNR , but the overall distribution has little correlation either with the distortion of the SNR boundary or with the distribution of radio brightness . Along the eastern boundary , where the SNR was considered to be interacting with molecular clouds in previous studies , we have not found any strong 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 northern area , the broad-line emitting cloud is composed of a small ( \sim 2 ^ { \prime } or 0.5 pc ) , very bright , U-shaped part and several clumps scattered around it . There is a significant enhancement of radio emission with flat ( -0.28 \pm 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 \sim 30 ^ { \prime } in extent . Small ( \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 1 ^ { \prime } .2 or 0.3 pc ) , bright clumps are seen along the filamentary structure . We have obtained sensitive J=1–0 and J=2–1 spectra of ^ { 12 } CO and ^ { 13 } CO molecules toward several peak positions . The intensity of ^ { 12 } CO J=2–1 emission is low ( T _ { mb } < 7 K ) and the ratio of ^ { 12 } CO J=2–1 to J=1–0 integrated intensities is high ( 1.6–2.3 ) , which suggests that the emission is from warm , dense , and clumpy gas . We have applied an LVG analysis to derive their physical parameters . The detected broad CO lines are believed to be emitted from the fast-moving molecular gas swept-up by the SNR shock . The small ( \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 20 km s ^ { -1 } ) shock velocity suggests that the shock is a non-dissociating C-shock . We discuss the correlation of the shocked molecular gas with the previously detected , shocked atomic gas and the associated infrared emission .