We report on a study of electric field-induced doping of the highly conductive ruthenate SrRuO3 using an ionic liquid as the gate dielectric in a field-effect transistor configuration. Two distinct carrier transport regimes are identified for increasing positive gate voltage in thin (10 nm) films grown heteroepitaxially on SrTiO3 substrates. For Vg = 2 V and lower, the sample shows an increased conductivity of up to 13%, as might be expected for electron doping of a metal. At higher Vg = 2.5 V, we observe a large decrease in electrical conductivity of >20% (at 4.2 K) due to the prevalence of strongly blocked conduction pathways.