We discuss the importance of the three-nucleon isospin T = 3/2 component in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the Av18 nucleon-nucleon potential alone or combined with the Urbana IX three-nucleon force as well as the locally regularized chiral (NLO)-L-4 nucleon-nucleon potential alone or supplemented by the chiral (NLO)-L-2 three-nucleon force. We find that the isospin T = 3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the S-1(0) state with isospin T = 3/2. For neutron-deuteron elastic scattering the T = 3/2 contributions are insignificant and charge-independence breaking can be accounted for by neglecting T = 3/2 component and using the effective t-matrix generated with the so-called "2/3 - 1/3" rule.