A hydrazinium ṄH-NH_{3}^{+} radical was identified by ESR in γ-irradiated Li(N_{2}H_{5})SO_{4} single crystal. Unpaired electron is strongly localized on the nitrogen atom as compared to hydrazinium radicals in other crystals. Angular variations of the multicomponent ESR spectra and computer calculations gave the isotropic hyperfine coupling parameters (in mT): a_{N1} = 1.93, a_{N2} = 0.80, a_{H1} = 2.50, a_{H1'} = 0.48 (NH_{3}), and a_{H2} = 1.40 (adjacent molecule). The radiation defects containing unpaired electrons do not influence much the protonic conductivity along the hydrazine molecule chains in the crystal. It confirms a tunelling mechanism of the conductivity activated by NH_{2}-group rotation. Spin-lattice relaxation time T_{1} varies strongly with temperature in the range from 100 ms (10 K) to 90 μs (170 K) and is governed by spectral diffusion (1/T_{1} ∝ T^{2}) and a Murphy-type mechanism (1/T_{1} ∝ cosech(Δ/T)) with Δ = 150 cm^{-1}. A distribution of the spin-relaxation times was observed with temperature independent dispersion parameter β = 0.76.