We measure the time-dependent CP asymmetry in B^0→K_S^0π^0γ decays for two regions of K_S^0-π^0 invariant mass, m(KS0π0), using the final BABAR data set of 467×10^6 BB pairs collected at the PEP-II e^+e^- collider at SLAC. We find 339±24 B^0→K^(*0)γ candidates and measure S_(K*γ)=-0.03±0.29±0.03 and C_(K*_γ)=-0.14±0.16±0.03. In the range 1.1<m(K_S^0π^0)<1.8 GeV/c^2 we find 133±20 B^0→K_S^0π^0γ candidates and measure S_(KS^0π^0γ)=-0.78±0.59±0.09 and C_(KS^0π^0γ)=-0.36±0.33±0.04. The uncertainties are statistical and systematic, respectively
