Electrical connection device for a vehicle hitch assembly comprising: - a bundle for a plurality of electrical wires, - a casing comprising a body equipped with an opening closed by a cover, - a plug receiving said bundle of electrical wires and comprising a plurality of electrical connectors each connected to a wire of said bundle of wires and emerging on a coupling face of the plug, - an adaptor (18, 18') housed inside the body of the casing between said plug and the opening of the body, said adaptor comprising: - a connection face (180, 180') situated facing the cover in closed position, - a coupling face (182, 182') in contact against the coupling face of said plug, - a plurality of electrical connectors (184, 184'), one end of each electrical connector (184, 184') emerging on the connection face (180, 180') according to a predetermined arrangement scheme and another end of each electrical connector (184, 184') emerging on the coupling face (182, 182') and being conformed such that each electrical connector (184, 184') of the adaptor (18, 18') is linked electrically with an electrical connector of the plug, characterized in that the body is equipped with a removable bottom receiving an end of said bundle of electrical wires; is that said plug is housed inside the body of the casing. - a bundle for a plurality of electrical wires, - a casing comprising a body equipped with an opening closed by a cover, - a plug receiving said bundle of electrical wires and comprising a plurality of electrical connectors each connected to a wire of said bundle of wires and emerging on a coupling face of the plug, - an adaptor (18, 18') housed inside the body of the casing between said plug and the opening of the body, said adaptor comprising: - a connection face (180, 180') situated facing the cover in closed position, - a coupling face (182, 182') in contact against the coupling face of said plug, - a plurality of electrical connectors (184, 184'), one end of each electrical connector (184, 184') emerging on the connection face (180, 180') according to a predetermined arrangement scheme and another end of each electrical connector (184, 184') emerging on the coupling face (182, 182') and being conformed such that each electrical connector (184, 184') of the adaptor (18, 18') is linked electrically with an electrical connector of the plug, characterized in that the body is equipped with a removable bottom receiving an end of said bundle of electrical wires; is that said plug is housed inside the body of the casing. - a connection face (180, 180') situated facing the cover in closed position, - a coupling face (182, 182') in contact against the coupling face of said plug, - a plurality of electrical connectors (184, 184'), one end of each electrical connector (184, 184') emerging on the connection face (180, 180') according to a predetermined arrangement scheme and another end of each electrical connector (184, 184') emerging on the coupling face (182, 182') and being conformed such that each electrical connector (184, 184') of the adaptor (18, 18') is linked electrically with an electrical connector of the plug, characterized in that the body is equipped with a removable bottom receiving an end of said bundle of electrical wires;