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We present a formalism to obtain equilibrium configurations of uniformlyrotating fluid in the second post-Newtonian approximation of generalrelativity. In our formalism, we need to solve 29 Poisson equations, but theirsource terms decrease rapidly enough at the external region of the matter(i.e.,at worst $O(r^{-4})$). Hence these Poisson equations can be solved accuratelyas the boundary value problem using standard numerical methods.This formalismwill be useful to obtain nonaxisymmetric uniformly rotating equilibriumconfigurations such as synchronized binary neutron stars just before mergingand the Jacobi ellipsoid.Comment: 25 pages including 3 tables, REVTeX, 1 postscript figure included; to  appear in Physical Review

Formulation for nonaxisymmetric uniformly rotating equilibrium configurations in the second post-Newtonian approximation of general relativity