Do psi(4040), psi(4160) signal hybrid charmonium?

We suggest that psi(4040) and psi(4160) are strong mixtures of ground state hybrid charmonium at similar to 4.1 GeV and the psi(3S) of conventional charmonium. The Gamma(e+e-), masses and total widths of the psi(4040) and psi(4160) are in accord with this hypothesis. Their hadronic decays are predicted to be dominated by the psi(3S) component and hence are correlated. In particular we find a spin counting relation Gamma(4160 --> DsDs*) similar to 4 Gamma(4040 --> DsDs) due to their common psi(3S) component. For D and D* production, using psi(4040) branching ratios as input, we predict that the decay pattern of the psi(4160) will be very different from that of the psi(4040). These predictions may be tested in historical data from SPEAR, BES or at future Tau-Charm Factories.