  The symmetry properties of the Cooper pairing problem for multi-component
ultra-cold dipolar molecular systems are investigated. The dipolar anisotropy
provides a natural and robust mechanism for both triplet and singlet Cooper
pairing to first order in the interaction strength. With a purely dipolar
interaction, the triplet $p_z$-like polar pairing is the most dominant. A
short-range attractive interaction can enhance the singlet pairing to be nearly
degenerate with the triplet pairing. We point out that these two pairing
channels can mix by developing a relative phase of $\pm\frac{\pi}{2}$, thus
spontaneously breaking time-reversal symmetry. We also suggest the possibility
of such mixing of triplet and singlet pairing in other systems.
