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.
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