In this article dimension reduction is used to derive the form of the free energy of a thin film made of a non simple material of grade two. Let \(\Omega_\varepsilon=\omega\times (-\frac\varepsilon2,\frac\varepsilon2)\), where \(\omega\subset\mathbb{R}^2\) is open, bounded and connected, \(\varepsilon\) is a small positive number. The energy of the body is \[ I_\varepsilon:u\in W^{2,p}(\Omega_\varepsilon)\to \int_{\Omega_\varepsilon} W(D^2 u)dx \] which should be minimized over \[ {\mathcal B}_\varepsilon = \left\{u\in W^{2,p}(\Omega_\varepsilon\mathbb{R}^3): u(x)=x \;\text{on}\;\partial \omega\times(-\frac\varepsilon2,\frac\varepsilon2) \right\}, \] where \(W: Sym(\mathbb{R}^3)\to\mathbb{R}\) is a bulk energy density. The goal is to study the \(\Gamma-\)limit of this minimization problem for \(\varepsilon\to 0\). Using Young measures the authors obtain in the limit a Cosserat model for the thin film.