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NaTiSi2O6 is an exemplary compound, showing an orbital assisted spin-Peierls phase transition at Tc = 210 K. We present the results of 29Si and 23Na NMR measurements of NaTiSi2O6. The use of magic angle spinning techniques unambiguously shows that only one dynamically averaged silicon site can be seen at T > Tc. At cooling, the 29Si MAS NMR spectrum shows interesting changes. Immediately below Tc the spectrum gets very broad. Cooling further, it shows two broad lines of unequal intensities which become narrower as the temperature decreases. Below 70 K two narrow lines have chemical shifts that are typical for diamagnetic silicates. The hyperfine field values for the two sites are 7.4 kOe/kB and 4.9 kOe/kB. In the paramagnetic state at high temperature, the spin-lattice relaxation of 29Si was found to be weakly temperature dependent. Below Tc the Arrhenius type temperature dependence of the relaxation rate indicates an energy gap D/kB = 1000(50) K. In the temperature region from 120 to 300 K the relaxation rate was strongly frequency dependent. At room temperature we found a power law dependence on Larmor frequency of -0.65(5). For 70 < T < 120 K the relaxation appeared to be non-exponential which we assigned to a relaxation due to fixed paramagnetic centers. Simulation of the magnetization recovery curve showed a temperature dependence of the concentration of these centers proportional to the magnetic susceptibility. The NMR spectrum of 23Na shows the line with typical shape for the central transition of a quadrupolar nucleus. A small frequency shift of 23Na resonance corresponds to a very small hyperfine field of 0.32 kOe/kB . In addition, at T > Tc the 23Na spectrum shows another Lorentzian shaped resonance which we attribute to the Na sites where the quadrupolar coupling is partly averaged out by ionic motion.