  The one-loop contributions to the chromomagnetic dipole moment
$\hat\mu_t(q^2)$ and electric dipole moment $\hat d_t(q^2)$ of the top quark
are calculated within the reduced 331 model (RM331) in the general case of an
off-shell gluon. It is argued that the results are gauge independent for
$q^2\ne 0$ and represent valid observable quantities. In the RM331 $\hat
\mu_t(q^2)$ receives new contributions from two heavy gauge bosons $Z'$ and
$V^+$ and a new neutral scalar boson $h_2$, along with a new contribution from
the standard model Higgs boson via flavor changing neutral currents. The
latter, which are also mediated by the $Z'$ gauge boson and the scalar boson
$h_2$, can give a non-vanishing $\hat d_t$ provided that there is a
$CP$-violating phase. The analytical results are presented in terms of both
Feynman parameter integrals and Passarino-Veltman scalar functions, which are
useful to cross-check the numerical results. Both $\hat\mu_t(q^2)$ and $\hat
d_t$ are numerically evaluated for parameter values still allowed by the
constraints from experimental data. It is found that the new one-loop
contributions of the RM331 to $\hat \mu_t(q^2)$ are of the same order of
magnitude or larger than in other standard model extensions, with the dominant
contribution arising from the $V^+$ gauge boson for $\|q\|$ in the 30-1000 GeV
interval and a mass $m_{V}$ of the order of a few hundreds of GeVs. As for
$\hat d_t(q^2)$, it receives the largest contribution from $h_2$ exchange and
can reach values of the order of $10^{-20}$, which is smaller than the
contributions predicted by other standard model extensions.
