Many extended models of particle physics that explain non-zero neutrino mases also include non-standard interactions (NSI) of
these elusive particles with other fermions. The NSIs that modify the collisions between neutrinos and electrons have an impact on the process of
neutrino decoupling in the early universe, leading to a different contribution to the radiation energy density, parameterised by the effective number of neutrinos, $N_{\rm eff}$. We have performed an analysis of the influence of non-universal and flavour-changing NSI on $N_{\rm eff}$, both for one-parameter and multi-parameter choices. In comparison with current constraints from terrestrial experiments, cosmology is less sensitive to NSI parameters, but future cosmological observations could provide competitive and complementary bounds for some combinations of NSI couplings.