  This paper reports on the search for heavy neutrinos with masses in the range
$140 < M_N < 493$ MeV/c$^2$ using the off-axis near detector ND280 of the T2K
experiment. These particles can be produced from kaon decays in the standard
neutrino beam and then subsequently decay in ND280. The decay modes under
consideration are $N \to \ell^{\pm}_{\alpha} \pi^{\mp}$ and $N \to
\ell^+_{\alpha} \ell^-_{\beta} \nu (\bar\nu)$ ($\alpha,\beta=e,\mu$). A search
for such events has been made using the Time Projection Chambers of ND280,
where the background has been reduced to less than two events in the current
dataset in all channels. No excess has been observed in the signal region. A
combined Bayesian statistical approach has been applied to extract upper limits
on the mixing elements of heavy neutrinos to electron-, muon- and tau-
flavoured currents ($U_e^2$, $U_{\mu}^2$, $U_{\tau}^2$) as a function of the
heavy neutrino mass, e.g. $U_e^2 < 10^{-9}$ at $90\%$ C.L. for a mass of $390$
MeV/c$^2$. These constraints are competitive with previous experiments.
