A study of the behavior of the response functions of the [C4mim] [BF4] + water ionic binary solution near its liquid-liquid critical point at atmospheric pressure is presented. Phase equililibrium temperatures, which allow to obtain the critical coordinates of this system, are determined. Measurements of the isobaric heat capacity per unit volume in the critical region indicate Ising-like behavior. The slope of the critical line, (dT/dp)c, is estimated by means of Prigogine and Defay's equation using experimentally determined excess volumes and excess enthalpies as a function of temperature. (dT/dp)c is found to be near zero. The consequences of this fact for the global critical behavior of second-order volumetric derivatives are discussed.