We report electronic transport measurements on single crystals of NaFe$_{1-x}$Co$_x$As system. We found that the cotangent of Hall angle, cot$theta_{rm H}$, follows $T^4$ for the parent compound with filamentary superconductivity and $T^2$ for the heavily-overdoped non-superconducting sample. While it exhibits approximately $T^3$-dependence in all the superconducting samples, suggesting this behaivor is associated with bulk superconductivity in ferropnictides. A deviation develops below a characteristic temperature $T^*$ well above the structural and superconducting transitions, accompanied by a departure from power-law temperature dependence in resistivity. The doping dependence of $T^*$ resembles the crossover line of pseudogap phase in cuprates.