Greater Cooperation with Local Governments in Water Project Analysis Act - Requires the Secretary concerned (the Secretary of Interior with respect to activities of the Bureau of Reclamation and the Secretary of the Army with respect to activities of the Corps of Engineers) to treat a qualified local government, upon request, as if such government is a federal agency afforded the status of a cooperating agency for purposes of an analysis under the National Environmental Policy Act of 1969 of any water project undertaken by the Bureau or the Corps that would result in initial or increased diversion of water from the basin of one river to the basin of any other river.