We present a measurement of the branching fraction and time-dependent C P asymmetry of B 0 → ρ 0 K 0 . The results are obtained from a data sample of 227 × 10 6 Υ ( 4 S ) → B ¯¯¯ B decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at Stanford Linear Accelerator Center. From a time-dependent maximum likelihood fit yielding 111 ± 19 signal events, we find B ( B 0 → ρ 0 K 0 ) = ( 4.9 ± 0.8 ± 0.9 ) × 10 − 6 , where the first error is statistical and the second systematic. We report the measurement of the C P parameters S ρ 0 K 0 S = 0.20 ± 0.52 ± 0.24 and C ρ 0 K 0 S = 0.64 ± 0.41 ± 0.20 .