The electrical properties of polycrystalline aluminum nitride (AlN) films grown by reactive dc magnetron sputtering are investigated in the transient and the steady-state regimes through metal-insulator-metal (MIM) structures with molybdenum (Mo) as metal electrodes. Measurements of current-time, current-voltage, and current-temperature characteristics are performed on AlN MIM structures. The extracted dielectric constant is 9.9. The transient current is observed to follow the empirical Curie–Von Schweidler law and its dependence on the applied field and the operating temperature is modeled. The time approach result is compared with the frequency-approach result by measuring the permittivity dispersion for low frequencies. Also, all the leakage mechanisms in AlN are identified in the steady-state regime depending on the applied field range. For a low electric field, the conduction mechanism is the Ohmic regime and the AlN resistivity is estimated to be 2.1×1015 Ω cm at room temperature. For higher electric fields, the ionic conduction is observed to be the dominant mechanism while the Poole–Frenkel transport is identified in the breakdown (BD) vicinity. A statistical approach is used to study the BD strength of the AlN through the Weibull distribution. The critical field for the dielectric BD ranges from 4.64 to 5.84 MV cm−1.