We report the first quantitative analysis of the Fe K-edge polarized x-ray absorption near edge structure of the iron protein carbonmonoxy-myoglobin (MbCO) single crystal and of its cryogenic photoproduct Mb(*)CO. The CO-Fe-heme local structure has been determined using a novel fitting procedure based on the full multiple scattering approach. The extracted local structure of Mb(*)CO includes a Fe-CO distance of (3.08+/-0.07) A, with a tilting angle between the heme normal and the Fe-C vector of (37+/-7) degrees, and a bending angle between the Fe-C vector and the C-O bond of (31+/-5) degrees.