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We analyze the quasi-two-body decays B→Kρ→Kππ in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the P-wave states ρ(770) and ρ′(1450) are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct CP asymmetries of the B→Kρ(770),Kρ′(1450)→Kππ modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the P-wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the B→Kρ(770)→Kππ decays supports the PQCD factorization framework for exclusive hadronic B meson decays.