  We discuss and compare the charge-parity (CP) asymmetry in the charged Higgs
boson decays H -> \bar{u}_i d_j for the second and third generation quarks in
the minimal supersymmetric standard model. As part of the analysis, we derive
some general analytical formulas for the imaginary parts of two-point and
three-point scalar one-loop integrals and use them for calculating vectorial
and tensorial type integrals needed for the problem under consideration. We
find that, even though each decay mode has a potential to yield a CP asymmetry
larger than 10%, further analysis based on the number of required charged Higgs
events at colliders favors the \bar{t}b, \bar{c}b, and \bar{c}s channels, whose
asymmetry could reach 10-15% in certain parts of the parameter space.
