  We compute the order $\alpha_s$ QCD corrections to the density matrix for the
decay of a neutral Higgs boson $\phi$ with (in)definite CP parity into a quark
antiquark pair, respectively the QED corrections for the decay into a pair of
charged leptons. We classify and calculate single spin asymmetries and
spin-spin correlations which are generated by the scalar and pseudoscalar
Yukawa couplings. These spin effects can be traced in $\phi \to \tau^-\tau^+$
and, for heavy Higgs bosons, in $\phi \to t\bar{t}$. We also calculate
resulting correlations among the final states and estimate, for the respective
decay modes, the number of events needed to measure the Yukawa couplings with
these correlations at the 3 sigma level.
