  We consider the Schr\"odinger functional with staggered one-component
fermions on a fine lattice of size $(L/a)^3 \times (T/a)$ where $T/a$ must be
an odd number. In order to reconstruct the four-component spinors, two
different set-ups are proposed, corresponding to the coarse lattice having size
$(L/2a)^3 \times (T'/2a)$, with $T' = T \pm a$. The continuum limit is then
defined at fixed $T'/L$. Both cases have previously been investigated in the
pure gauge theory. Here we define fermionic correlation functions and study
their approach to the continuum limit at tree-level of perturbation theory.
