The vibrational properties of monoclinic dirutile-type CoTeO4 (space group P21/c) were investigated by means of Raman and infrared (IR) spectroscopy on stoichiometric single crystals and theoretical density-functional theory (DFT) calculations. Experimental in situ investigations under pressure and temperature variations up to 10.1 GPa and 750 K confirmed the singular phase stability of the monoclinic lattice and the absence of any structural transition. The IR spectra exhibit modes that are not observed in the Raman spectra, thus offering a comprehensive understanding of the vibrational behavior of the title compound. The symmetry and degeneracy of modes and their contributions to the overall vibrational spectrum of CoTeO4 were analyzed using group theory. DFT calculations were performed both on a cluster level and based on the crystal structure of monoclinic CoTeO4 in order to gain further insights into the vibrational properties. The calculated vibrational frequencies and modes were compared with the experimental data, allowing for a detailed investigation of the lattice dynamics and the nature of the vibrational modes in CoTeO4, and are corroborated with the analytical Wilson's F-G matrix method. These findings provide fundamental insights into the crystal symmetry and lattice dynamics of CoTeO4. The results are discussed and compared to those of isoformular systems.