We present a measurement of the time-dependent CP asymmetry in the radiative-penguin decay B0 to KS pi+ pi- gamma, using a sample of 470.9 million Upsilon(4S) to BBbar events recorded with the BaBar detector at the Pep-II e+e- storage ring at SLAC. Using events with m(K pi pi)<1.8 GeV/c^2, 0.60.945 GeV/c^2, we obtain the CP-violating parameters S(KS pi+ pi- gamma) = 0.137 pm 0.249 + 0.042 - 0.033 and C(KS pi+ pi- gamma) = -0.390 pm 0.204 + 0.045 - 0.050, where the first quoted errors are statistical and the second are systematic. We extract from this measurement the time-dependent CP asymmetry related to the hadronic CP eigenstate $rho^0 KS$ and obtain S(KS Rho0 gamma) = 0.249 pm 0.455 + 0.076 - 0.060. This observable provides information on the photon polarization in the underlying $b to s gamma$ transition. To extract S(KS Rho0 gamma) from S(KS pi+ pi- gamma), assuming isospin symmetry, we study B+ to K+ pi+ pi- gamma decays and measure intermediate resonant amplitudes of different resonances decaying to $Kpipi$ through the intermediate states Rho0 K+, Kstar0 pi+ et (K pi) S-wave pi+. In addition to the need of this information for the extraction of S(KS pi+ pi- gamma), it provides input on the B to K pi pi system, which is useful for other studies of the photon polarization. The fractions of the different Kres to K pi pi states as well as the overall fractions of the Rho0 K+, Kstar0 pi+ et (K pi) S-wave pi+ components are also measured.
