  We consider non-Hermitian Dirac operators in QCD-like theories coupled to a
chiral U(1) potential or an imaginary chiral chemical potential. We show that
in the continuum they fall into the recently discovered universality classes
AI$^\dagger$ or AII$^\dagger$ of random matrix theory if the fermions transform
in pseudoreal or real representations of the gauge group, respectively. For
staggered fermions on the lattice this correspondence is reversed. We verify
our predictions by computing spacing ratios of complex eigenvalues, whose
distribution is universal without the need for unfolding.
