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Ilmenite-type crystals find a variety of technological applications due to their intriguing physical properties. We present the results of the lattice dynamics studies of honeycomb antiferromagnetic ilmenite CoTiO$_3$ single crystal by the complementary polarized infrared, Raman, and dielectric spectroscopic techniques that are supplemented by the DFT calculations. The frequencies and symmetries of all predicted infrared and Raman active phonons were uniquely identified. Furthermore, it was found that the dielectric permittivity demonstrates distinct changes below antiferromagnetic ordering temperature in zero magnetic field due to spontaneous magnetodielectric effect. Our results establish the reliable basis for further investigation of the coupling of phonons with spins, magnetic excitations and other physical phenomena of this promising material.