  We mapped 12CO J=1-0, 12CO J=2-1, 13CO J=1-0, and 13CO J=2-1 lines toward
supernova remnant (SNR) Cassiopeia A with the IRAM 30m telescope. The molecular
clouds (MCs) along the line of sight of Cas A do not show optically thin,
shock-broadened 12CO lines ($\Delta V \le 7$ km s$^{-1}$ toward Cas A), or
high-temperature features from shock heating ($T_k \le 22$ K toward Cas A).
Therefore, we suggest that there is no physical evidence to support that the
SNR is impacting the molecular gas. All the detected MCs are likely in front of
Cas A, as implied by the HCO+ absorption line detected in the same velocity
ranges. These MCs contribute H$_2$ column densities of $5\times 10^{21}$
cm$^{-2}$, $5\times 10^{21}$ cm$^{-2}$, and $2\times 10^{21}$ cm$^{-2}$ in the
west, south, and center of the SNR, respectively. The 20 K warm gas at
$V_{LSR}\sim -47$ km s$^{-1}$ is distributed along a large-scale molecular
ridge in the south of Cas A. Part of the gas is projected onto Cas A, providing
a foreground H$_2$ mass of $\sim 200 (d/3 kpc)^2$ Msun, consistent with the
mass of cold dust (15--20 K; 2--4 Msun) found in front of the SNR. We suggest
that the 20 K warm gas is heated by background cosmic rays with an ionization
rate of $\zeta({\rm H_2})\sim 2\times 10^{-16}$ s$^{-1}$. The cosmic rays or
X-ray emission from Cas A are excluded as the heating sources of the clouds.
