We present a measurement of the branching fraction and time-dependent CP violation parameters for B-0 ->(D*+D*-KS0) decays. These results are obtained from a 414 fb(-1) data sample that contains 449x10(6) B (B) over bar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We obtain the branching fraction, B(B-0 ->(D*+D*-KS0))=[3.4 +/- 0.4(stat)+/- 0.7(syst)]x10(-3), which is in agreement with the current world average. We also obtain an upper limit on the product branching fraction for a possible two-body decay, B(B-0 -> D-s1(+)(2536)D*-)B(D-s1(+)(2536)->(D*+KS0))< 7.1x10(-4) (90% CL). In the traditional 2-parameter time-dependent CP analysis, we measure the CP violation parameters, A(CP)=-0.01(-0.28)(+0.28)(stat)+/- 0.09(syst), Dsin2 phi(1)=0.06(-0.44)(+0.45)(stat)+/- 0.06(syst). No evidence for either mixing-induced or direct CP violation is found. In a 3-parameter fit sensitive to cos2 phi(1) performed in the half-Dalitz spaces, s(-)<= s(+) and s(-)> s(+), where s(+/-)equivalent to m(2)((DKS0)-K-*+/-), we extract the CP violation parameters, J(c)/J(0)=0.60(-0.28)(+0.25)(stat)+/- 0.08(syst), 2J(s1)/J(0)sin2 phi(1)=-0.17(-0.42)(+0.42)(stat)+/- 0.09(syst), 2J(s2)/J(0)cos2 phi(1)=-0.23(-0.41)(+0.43)(stat)+/- 0.13(syst). A large value of J(c)/J(0) would indicate a significant resonant contribution from a broad unknown D-s(**+) state. Although the sign of the factor, 2J(s2)/J(0), can be deduced from theory, no conclusion can be drawn regarding the sign of cos2 phi(1) given the errors.