EU Tauri is a classical Cepheid with one of the shortest period known. A Fourier decomposition study of its V light curve by Simon S Lee (1981) revealed a peculiar position in phase-period diagrams, very similar to the star SU Cas which is probably an overtone pulsator (Gieren, 1982). This suggested the possibility that EU Tau might be another galactic overtone pulsator. In order to investigate this question, some 100 new photometric observations of this star on the UBVRI (Johnson) system were obtained with the #2 0.9m telescope of KPNO. Simultaneously, 43 CCD spectra of the star were secured on the Coudé feed telescope of KPNO which were measured for radial velocities using a correlation technique. These velocities have an internal accuracy of better than 0.5 km/s and define a complete velocity curve of EU Tau.