An infrared double-resonance laser spectroscopic technique is used to study state-resolved rotational energy transfer (RET), vibration-vibration (V-V) transfer, and symmetry-exchanging collisions in asymmetrically deuterated methane (CHD3). The molecules are prepared in selected rovibrational states of the {upsilon3, upsilon6} = 1 dyad using coincidences between CO2 laser lines and dyad<--ground state transitions. Measurements of both the total rate of depopulation by collisions and the rates of transfer into specific rovibrational (upsilon,J,K) levels are carried out using time-resolved tunable diode laser absorption spectroscopy. Total excited-state depopulation and ground-state recovery rates range from 0.5 to 1.0 times the Lennard-Jones collision rate, consistent with relaxation due to short-range forces. V-V (nu6-->nu3) processes contribute about 10% of the total relaxation rate, and symmetry-changing (A<-- -->E) collisions occur at a rate another order of magnitude smaller, viz. (0.17+/-0.02) mus-1 Torr-1, corresponding to an effective cross section of 0.64 angstrom2, around 10(-2) sigma(LJ). The symmetry-exchanging collision efficiency for CHD3 as well as for other systems reported elsewhere (CD3Cl,CH3F) can be quantitatively estimated using a simple Forster resonant exchange mechanism. The state-to-state RET rates are modeled using a kinetic master equation. A strong propensity rule, DELTAK = +/-3x (integer), similar to that found for highly dipolar symmetric tops such as ammonia, applies to CHD3 as well. We conclude that the flow of energy and angular momentum in molecular relaxation is dominated by the internal level structure of the molecule, rather than by specific details of the intermolecular potential.