  We performed $^{59}$Co nuclear magnetic and quadrupole resonance (NMR and
NQR) measurements under pressure on a single-crystalline CeCoSi, which
undergoes an unresolved phase transition at $T_0$. The NQR spectra clearly
showed that the phase transition at $T_0$ is nonmagnetic, but any symmetry
lowering at the Co site was not seen irrespective of the feature of
second-order phase transition. By contrast, the NMR spectra were split by the
induced magnetic field perpendicular to the external magnetic field. These
results show that the phase below $T_0$ is not a simple paramagnetic state but
is most likely electric multipolar ordered state of Ce $4f$ electrons. The
development of the Kondo effect by applying pressure is thought to be crucial
to stabilize this state and to show novel features beyond commonality of
tetragonal Ce-based systems.
