We have measured the terahertz frequency-dependent sheet conductivity and its transient response following femtosecond optical excitation for single-layer graphene samples grown by chemical vapor deposition. The conductivity of the unexcited graphene sheet, which was spontaneously doped, showed a strong free-carrier response. The THz conductivity matched a Drude model over the available THz spectral range and yielded an average carrier scattering time of 70 fs. Upon photoexcitation, we observed a transient decrease in graphene conductivity. The THz frequency-dependence of the graphene photoresponse differs from that of the unexcited material but remains compatible with a Drude form. We show that the negative photoconductive response arises from an increase in the carrier scattering rate, with a minor offsetting increase in the Drude weight. This behavior, which differs in sign from that reported previously for epitaxial graphene, is expected for samples with relatively high mobilities and doping levels. The photoinduced conductivity transient has a picosecond lifetime and is associated with nonequilibrium excitation conditions in the graphene.