We present a measurement of RK∗, the branching fraction ratio B(B→K∗μ+μ-)/B(B→K∗e+e-), for both charged and neutral B mesons. The ratio for the charged case RK∗+ is the first measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass q2. The analysis is based on a data sample of 711 fb-1, containing 772×106 BB¯ events, recorded at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The obtained results are consistent with standard model expectations.