  We give Chern-Weil definitions of the Maslov indices of bundle pairs over a
Riemann surface \Sigma with boundary, which consists of symplectic vector
bundle on \Sigma and a Lagrangian subbundle on \partial{\Sigma} as well as its
generalization for transversely intersecting Lagrangian boundary conditions. We
discuss their properties and relations to the known topological definitions. As
a main application, we extend Maslov index to the case with orbifold interior
singularites, via curvature integral, and find also an analogous topological
definition in these cases.
