We study the decay B0→D*+D*-KS0 using (230±2) ×106BB̄ pairs collected by the BABAR detector at the PEP-II B factory. We measure a branching fraction B(B0→D*+D*-KS0)=(4. 4±0.4±0.7)×10-3 and find evidence for the decay B0→D*-Ds1+(2536) with a significance of 4.6σ. A time-dependent CP asymmetry analysis is also performed to study the possible resonant contributions to B0→D*+D*-KS0 and the sign of cos2β. Our measurement indicates that there is a sizable resonant contribution to the decay B0→D*+D*-KS0 from an unknown Ds1+ state with large width, and that cos2β is positive at the 94% confidence level under certain theoretical assumptions. © 2006 The American Physical Society.