  Recent works have revealed that the recipe for field-antifield quantization
of Lagrangian gauge theories can be considerably relaxed when it comes to
choosing a path integral measure \rho if a zero-order term \nu_{\rho} is added
to the \Delta operator. The effects of this odd scalar term \nu_{\rho} become
relevant at two-loop order. We prove that \nu_{\rho} is essentially the odd
scalar curvature of an arbitrary torsion-free connection that is compatible
with both the anti-Poisson structure E and the density \rho. This extends a
previous result for non-degenerate antisymplectic manifolds to degenerate
anti-Poisson manifolds that admit a compatible two-form.
