An electronically coarse-grained model for water reveals a persistent vestige of the liquid-gas transition deep into the supercritical region. A crossover in the density dependence of the molecular dipole arises from the onset of nonpercolating hydrogen bonds. The crossover points coincide with the Widom line in the scaling region but extend farther, tracking the heat capacity maxima, offering evidence for liquidlike and gaslike state points in a "one-phase" fluid. The effect is present even in dipole-limit models, suggesting that it is common for all molecular liquids exhibiting dipole enhancement in the liquid phase.