We study the decay B 0 → D * + D * − K 0 S using ( 230 ± 2 ) × 10 6 B ¯¯¯ B pairs collected by the BABAR detector at the PEP-II B factory. We measure a branching fraction B ( B 0 → D * + D * − K 0 S ) = ( 4.4 ± 0.4 ± 0.7 ) × 10 − 3 and find evidence for the decay B 0 → D * − D + s 1 ( 2536 ) with a significance of 4.6 σ . A time-dependent C P asymmetry analysis is also performed to study the possible resonant contributions to B 0 → D * + D * − K 0 S and the sign of cos  2 β . Our measurement indicates that there is a sizable resonant contribution to the decay B 0 → D * + D * − K 0 S from an unknown D + s 1 state with large width, and that cos  2 β is positive at the 94% confidence level under certain theoretical assumptions.