The intrinsic d.c. electrical resistivity ($\rho$) - measurable on single crystals only - is often the quantity first revealing the properties of a given material. In the case of CH$_3$NH$_3$PbI$_3$ perovskite measuring $\rho$ under white light illumination provides insight into the coexistence of extended and shallow localized states (0.1 eV below the conduction band). The former ones dominate the electrical conduction while the latter, coming from neutral defects, serve as a long-lifetime charge carrier reservoir accessible for charge transport by thermal excitation. Remarkably, in the best crystals the electrical resistivity shows a metallic behaviour under illumination up to room temperature, giving a new dimension to the material in basic physical studies.