Following the work of Canright, Girvin and Brass [Phys. Rev. Lett. 63 (1989) 2291], we scrutinize the fermionic mean-field theory for the two-dimensional s = 1/2 XY spin model of hard-core bosons. Using nonlocal vertex operators and fermion correlators in a constant magnetic field, we calculated the spin-spin correlations, which show a Bose condensation. The mean-field theory is appropriate not only for the ground state but also for the low-lying excited states.