  Suppose a heavy neutral Higgs or scalar boson $H$ is discovered at the LHC,
it is important to investigate its couplings to the standard model particles as
much as possible. Here in this work we attempt to probe the CP-even and CP-odd
couplings of the heavy Higgs boson to a pair of top quarks, through the decay
$H \to t\bar t \to b W^+ \bar b W^-$. We use the helicity-amplitude method to
write down the most general form for the angular distributions of the
final-state $b$ quarks and $W$ bosons. We figure out that there are 6 types of
angular observables and, under CP$\widetilde{\rm T}$ conservation,
one-dimensional angular distributions can only reveal two of them.
Nevertheless, the $H$ couplings to the
  $t\bar t$ pair can be fully determined by exploiting the one-dimensional
angular distributions. A Higgs-boson mass of 380 GeV not too far above the
$t\bar t$ threshold is illustrated with full details. With a total of $10^4$
events of $H \to t\bar t \to bW^+ \bar b W^+$, one can determine the couplings
up to 10-20 % uncertainties.
