Abstract: The nature of strange axial-vector mesons are not well understood and can be investigated in D meson decays. In this work, it is found that the experimental data of D⁰ → K^±K₁^∓(1270)(→ ρK or K^*π) in the D⁰ → K⁺K^-π⁺π^- mode, disagree with the equality relation under the narrow width approximation and CP conservation of strong decays. Considering more other results of K₁(1270) decays, the data of B(D⁰ → K^-K₁⁺(1270)(→ K^*0π⁺)) is probably overestimated by one order of magnitude. We then calculate the branching fractions of the corresponding processes with K₁(1400) in the factorization approach, and find B(D⁰ → K^-K₁⁺(1400)(→ K^*0π⁺)) is comparable to the predicted B(D⁰ → K^-K₁⁺(1270)(→ K^*0π⁺)) using the equality relation. Besides, we suggest to measure the ratios between K₁(1270) → ρK and K^*π or to test the equality relations in other D meson decay modes.