This dissertation presents a measurement of time-dependent CP-violating asymmetries and a measurement of the CP-odd parity fraction in the decay B0 -> D*+D*-. The measurements are derived from a data sample of 88 x 10^6 BBbar pairs collected by the BaBar detector at the PEP-II asymmetric-energy B Factory located at the Stanford Linear Accelerator Center. A one-dimensional angular analysis of the decay products measures the CP-odd fraction to be 0.063 +/- 0.055(stat) +/- 0.009(syst), indicating that the D*+D*- final state is mostly CP-even. The time-dependent CP asymmetry parameters Im(lambda_+) and |lambda_+| are determined from an analysis of the time-dependence of flavor-tagged B decays. One neutral B meson is fully reconstructed in a D*+D*- final state, while the other B is inclusively reconstructed in order to determine its flavor. The Standard Model predicts the CP asymmetry parameters Im(lambda_+) and |lambda_+| to be -sin(2beta) and 1, respectively, in the absence of penguin diagram contributions. They are determined to be 0.05 +/- 0.29(stat) +/- 0.10(syst) and 0.75 +/- 0.19(stat) +/- 0.02(syst), respectively, which corresponds to a 2.5 sigma deviation from Standard Model predictions with penguin contributions ignored.