Natomas Basin Flood Protection Improvements Act of 2013 - Modifies the project for flood damage reduction, American and Sacramento Rivers, California, to authorize the Secretary of the Army to construct improvements to flood damage reduction facilities adjacent to those rivers in the vicinity of Sacramento, substantially in accordance with the report of the Chief of Engineers entitled "American River Watershed (Common Features) Project, Natomas Basin, Sacramento and Sutter Counties, California," dated December 30, 2010, at a specified cost. Requires the nonfederal interest to receive credit for expenses and in-kind contributions incurred for planning, design, and construction of the project and acquisition of lands, easements, rights-of-way, relocations, and dredged material disposal areas for the project. Requires such credit to be applied toward the nonfederal share of the project or of any other project for which the nonfederal interest has entered into a cost-sharing agreement with the Secretary.