We present an updated measurement of time-dependent CP asymmetries and the CP-odd fraction in the decay B0-->D*+D*- using 232x10(6)BB pairs collected by the BABAR detector at the SLAC PEP-II B factory. We determine the CP-odd fraction to be 0.125+/-0.044(stat)+/-0.007(syst). The time-dependent CP asymmetry parameters C+ and S+ are determined to be 0.06+/-0.17(stat)+/-0.03(syst) and -0.75+/-0.25(stat)+/-0.03(syst), respectively. The standard model predicts these parameters to be 0 and -sin2beta, respectively, in the absence of penguin amplitude contributions.