The Hall effect is reported for MnTe films of different compositions and thicknesses in the range 25-150 nm. Both R(o) and R(s) exhibit a pronounced size effect. R(o) remains negative for the entire thickness range studied, while the sign of R(s) depends on the substrate temperature and the tellurium content in the films. The extraordinary Hall coefficient is found to be proportional to the square of the total film resistivity, which suggests that the asymmetric scattering process is predominant at room temperature.