  Ho\v{r}ava--Lifshitz gravity has covariance only under the
foliation-preserving diffeomorphism. This implies that the quantities on the
constant-time hypersurfaces should be regular. In the original theory, the
projectability condition, which strongly restricts the lapse function, is
proposed. We assume that a star is filled with a perfect fluid with no-radial
motion and that it has reflection symmetry about the equatorial plane. As a
result, we find a no-go theorem for stationary and axisymmetric star solutions
in projectable Ho\v{r}ava--Lifshitz gravity under the physically reasonable
assumptions in the matter sector. Since we do not use the gravitational action
to prove it, our result also works out in other projectable theories and
applies to not only strong gravitational fields, but also weak gravitational
ones.
