Quasi-2D organic charge-transfer salts k-(BEDT-TTF)2Cu2(CN)3 has been in the focus of recent scientific attention as a candidate for a quantum spin liquid. After the discovery of a relaxor-like dielectric response in k-(BEDT-TTF)2Cu2(CN)3 and ferroelectricity in k-(BEDT-TTF)2Cu[N(CN)2]Cl, these compounds have gained further attentions as a new class of ferroelectrics of purely electronic origin. Since k-(BEDT-TTF)2Cu[N(CN)2]Cl shows long-ranged ferroelectric order and antiferromagnetic order simultaneously, it is an ideal system to study the coupling between the spin, charge, and lattice degrees of freedom. Here, we propose a neutron scattering experiment on deuterated single crystals of k-(BEDT-TTF)2Cu[N(CN)2]Cl in order to search for phonon anomalies coupled with electronic ferroelectricity.