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Following up on a suggestion that decay to a dark matter fermion might explain the 4σ discrepancy in the neutron lifetime, we consider the implications of such a fermion on neutron star structure. We find that including it reduces the maximum neutron star mass to well below the observed masses. In order to recover stars with the observed masses, the (repulsive) self-interactions of the dark fermion would have to be stronger than those of the nucleon-nucleon interaction.