It is well known that the key factor determining the performance of thermoelectric materials is the figure of merit, which depends on the thermal conductivity (TC), electrical conductivity, and Seebeck coefficient (SC). The electric current must be zero when measuring the TC and SC to avoid the occurrence of measurement errors. In this study, the complex-variable method is used to analyze the thermoelectric field near an elliptic inhomogeneity in an open circuit, and the field distributions are obtained in closed form. Our analysis shows that an electric current inevitably exists in both the matrix and the inhomogeneity even though the circuit is open. This unexpected electric current seriously affects the accuracy with which the TC and SC are measured. These measurement errors, both overall and local, are analyzed in detail. In addition, an error correction method is proposed based on the analytical results.