  Analyzing test particles falling into a Kerr black hole, we study
gravitational waves in Brans-Dicke theory of gravity. First we consider a test
particle plunging with a constant azimuthal angle into a rotating black hole
and calculate the waveform and emitted energy of both scalar and tensor modes
of gravitational radiation. We find that the waveform as well as the energy of
the scalar gravitational waves weakly depends on the rotation parameter of
black hole $a$ and on the azimuthal angle.
  Secondly, using a model of a non-spherical dust shell of test particles
falling into a Kerr black hole, we study when the scalar modes dominate. When a
black hole is rotating, the tensor modes do not vanish even for a ``spherically
symmetric" shell, instead a slightly oblate shell minimizes their energy but
with non-zero finite value, which depends on Kerr parameter $a$. As a result,
we find that the scalar modes dominate only for highly spherical collapse, but
they never exceed the tensor modes unless the Brans-Dicke parameter
$\omega_{BD} \lsim 750 $ for $a/M=0.99$ or unless $\omega_{BD} \lsim 20,000 $
for $a/M=0.5$, where $M$ is mass of black hole.
  We conclude that the scalar gravitational waves with $\omega_{BD} \lsim$
several thousands do not dominate except for very limited situations
(observation from the face-on direction of a test particle falling into a
Schwarzschild black hole or highly spherical dust shell collapse into a Kerr
black hole). Therefore observation of polarization is also required when we
determine the theory of gravity by the observation of gravitational waves.
