New Johnson UBVRI and Cousins (RI)c photometry of EU Tau from three observatories are used to answer the outstanding questions surrounding the pulsation period of this short-period Cepheid. These data provide almost complete phase coverage of the pulsation cycle. It is confirmed that EU Tau is pulsating with a single period near 2.1 days in agreement with that found previously by Fernie. Confusion in the literature about the photometric indices of the comparison star BD 18959 deg near EU Tau is shown to arise largely from misidentifications of BD 18957 deg and BD 18959 deg. New radial velocities for EU Tau are reported and compared to earlier observations with CORAVEL. Contemporaneous radial velocities and photometric data are ideally suited to a surface-brightness analysis of this interesting Cepheid.