We examine the neutrino and cosmic ray spectra resulting from two models of fitting the spectral energy distribution (SED) of the blazar Mrk 421 using a self-consistent leptohadronic code. The γ -ray emission is attributed to either synchrotron radiation of ultra-high energy protons (LHs model) or to synchrotron radiation from electrons that result from photopion interactions of lower energy protons (LH π model). Although both models succeed in fitting satisfactorily the SED, the parameter values that they use result in significantly different neutrino and cosmic-ray spectra. For the LH π model, which requires high proton energy density, we find that the neutrino spectrum peaks at an energy Eν,peak = 3.3 PeV which falls well within the energy range of recent neutrino observations. While at the same time its peak flux is just under the sensitivity limit of IC-40 observations, it cannot produce ultra-high energy cosmic rays. In the LHs model, on the other hand, neutrinos are far from being detectable because of their low flux and peak energy at Eν,peak ≃ 100 PeV. However, the propagation of protons produced by the decay of escaping neutrons results in an ultra-high energy cosmic ray flux close to that observed by Pierre Augere, HiRes and Telescope Array at energies Ep ≃ 30 EeV.