It is well known thanks to J. P. Serre that a smooth projective variety of codimension 1 or 2 is Gorenstein if and only if it is a complete intersection. This is no longer true for codimension 3 smooth Gorenstein varieties. This observation suggests that codimension 3 Gorenstein varieties form a suitable class of varieties to study when investigating non-complete intersection Gorenstein varieties. Buchsbaum and Eisenbud proved that codimension 3 Gorenstein varieties arise as Pfaffians of skew-symmetric maps of vector bundles of odd ranks. In this talk, we investigate Calabi-Yau threefolds that appear as pfaffians of skew symmetric odd sized matrices of multi-homogeneous polynomials in 6-dimensional product of projective spaces. In particular, we classify all decomposable vector bundles giving rise to a 3-codimensional Pfaffian Calabi-Yau threefold. Moreover, we propose a method for computing their Hodge numbers and Chern classes.