Path Integral and Solutions of the Constraint Equations: The Case of   Reducible Gauge Theories
  It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace. 
R. Ferraro, M. Henneaux and M. Puchin