We present a fiber refractometer based on the implementation of overlapped Michelson interferometers; the refractometer allows simultaneous refractive index measurement at two sensing points for samples discrimination. The fiber refractometer uses the Fresnel reflection in each fiber tip of the overlapped interferometers to generate the interference signal. Experimental results, implementing the two sensing points, for discrimination between non-contaminated and contaminated distilled water are presented. Despite the simplicity of the presented system, resolution and repeatability of 3×10-4 and 5×10-4 are obtained in a dip and read experiment using both sensing points simultaneously for refractive index measurement.