The electric polarization, dielectric permittivity, magnetoelectric effect, heat capacity, magnetization and ac susceptibility of magnetite films and polycrystals were investigated. The electric polarization of magnetite films with saturation values between 4 and 8 mu C cm(-2) was found to vanish between 32 and 38 K, but in polycrystals no phase transition was detected in this range by heat capacity. Both types of samples showed magnetoelectric effects at low temperatures below a frequency-dependent crossover. This is interpreted as arising from multiferroic relaxor behavior.