We investigated negative photoconductivity in graphene using ultrafast terahertz techniques. Infrared transmission was used to determine the Fermi energy, carrier density, and mobility of p-type chemical vapor deposition graphene samples. Time-resolved terahertz photoconductivity measurements using a tunable mid-infrared pump probed these samples at photon energies between 0.35-eV and 1.55-eV, approximately one-half to three times the Fermi energy of the samples. Although interband optical transitions in graphene are blocked for pump photon energies less than twice the Fermi energy, we observe negative photoconductivity at all pump photon energies investigated, indicating that interband excitation is not required to observe this effect. Our results are consistent with a thermalized free-carrier population that cools by electron-phonon scattering, but are inconsistent with models of negative photoconductivity based on population inversion.