  Massive neutrinos have non-negligible impact on the formation of large-scale
structures. We investigate the impact of massive neutrinos on the halo assembly
bias effect, measured by the relative halo bias $\hat{b}$ as a function of the
curvature of the initial density peak $\hat{s}$, neutrino excess
$\epsilon_\nu$, or halo concentration $\hat{c}$, using a large suite of $\Sigma
M_\nu{=}0.0$ eV and $0.4$ eV simulations with the same initial conditions. By
tracing dark matter haloes back to their initial density peaks, we construct a
catalogue of halo twins that collapsed from the same peaks but evolved
separately with and without massive neutrinos, thereby isolating any effect of
neutrinos on halo formation. We detect a $2\%$ weakening of the halo assembly
bias as measured by $\hat{b}(\epsilon_\nu)$ in the presence of massive
neutrinos. As there exists a significant correlation between $\hat{s}$ and
$\epsilon_\nu$ ($r_{cc}{=}0.319$), the impact of neutrinos persists at a
reduced level~($0.1\%$) in the halo assembly bias measured by
$\hat{b}(\hat{s})$. However, we do not detect any neutrino-induced impact on
$\hat{b}(\hat{c})$, consistent with earlier studies and the lack of correlation
between $\hat{c}$ and $\epsilon_\nu$ ($r_{cc}{=}0.087$). We also discover an
analogous assembly bias effect for the neutrino haloes, whose concentrations
are anti-correlated with the large-scale clustering of neutrinos.
