  In this work, we analyze the three-body $B_{(s)} \to \eta_c(1S,2S) K \pi$
decays within the framework of the perturbative QCD approach (PQCD) under the
quasi-two-body approximation, where the kaon-pion invariant mass spectra are
dominated by the
$K_0^*(1430)^0,K_0^*(1950)^0,K^*(892)^0,K^*(1410)^0,K^*(1680)^0$ and
$K_2^*(1430)^0$ resonances. The time-like form factors are adopted to
parametrize the corresponding $S$, $P$, $D$-wave kaon-pion distribution
amplitudes for the concerned decay modes, which describe the final-state
interactions between the kaon and pion in the resonant region. The $K\pi$
$S$-wave component at low $K\pi$ mass is described by the LASS line shape,
while the time-like form factors of other resonances are modeled by the
relativistic Breit-Wigner function. We find the following main points: (a) the
PQCD predictions of the branching ratios for most considered $B \to
\eta_c(1S)(K^{*0}\to )K^+\pi^-$ decays agree well with the currently available
data within errors; (b) for ${\cal B}(B^0 \to \eta_c (K_0^*(1430)\to
)K^+\pi^-)$ and ${\cal B}(B^0 \to \eta_c K^+\pi^-({\rm NR}))$ (here NR means
nonresonant), our predictions of the branching ratios are a bit smaller than
the measured ones; and (c) the PQCD results for the $D$-wave contributions
considered in this work can be tested once the precise data from the future
LHCb and Belle-II experiments are available.
