The tungsten ditelluride WTe₂ was suggested to belong to the Weyl semimetal family. We studied ¹²⁵Te spin-lattice relaxation and NMR spectra in a WTe₂ single crystal within a large range from 28 K up to room temperature. Measurements were carried out on a Bruker Avance 500 NMR pulse spectrometer for the crystalline c axis directed in parallel and perpendicular to the magnetic field. Relaxation proved to be single-exponential. The relaxation time varied depending on the sample position in magnetic field and frequency offset. The relaxation rate increased about linearly with temperature below 70 K, however the dependence became nearly quadratic at higher temperatures. The relaxation rate within the total temperature range was fitted using a theoretical model developed in Ref. [41] for Weyl semimetals and assuming the decrease of the chemical potential with increasing temperature. The results obtained for ¹²⁵Te spin-lattice relaxation evidence in favor of the topological nontriviality of the WTe₂ semimetal. The ¹²⁵Te NMR spectra agreed with the occurrence of nonequivalent tellurium sites and varied insignificantly with temperature.