In this work we report the calculation of the total cross section for pion-production by the dispersion of neutrinos on nucleons. We use a consistent formalism for the intermediate resonance states of spin-$\frac{3}{2}$, taking care on the conditions imposed by the invariance on contact transformations and using the Sachs parametrization for the form factors. In addition, we incorporate states in the second resonance region up to 1.6 GeV and implement different approaches for all the dressed resonance propagators. In addition to the $\mathrm{\ensuremath{\Delta}}(1232)$, we include the ${N}^{*}(1440)$, ${N}^{*}(1535)$, and ${N}^{*}(1520)$ resonance contributions, and it is shown that this inclusion improves the description of the total cross section regarding a model where only the $\mathrm{\ensuremath{\Delta}}(1230)$ resonance is considered. Also, results for antineutrinos are properly described.