We show that experimental data on inclusive neutrino reactions can be used to obtain general bounds on the coupling constants of the isovector part of the hadronic weak neutral current provided this isovector current is related to the charged current by isospin rotation. These bounds are free from the assumption of a specific model for the neutral current as well as any dynamical assumption on the hadronic structure functions. We derive upper bounds on the coupling constants which involve only the cross sections for isospin-averaged nucleon target as well as lower bounds which require a knowledge of the cross sections for proton and neutron separately.