The Dalitz decays of the positive-parity DsJ(*) charmed mesons, DsJ(*)→Ds(*)ℓ+ℓ− with J=0, 1, 2 and ℓ=e, μ, are important processes to investigate the nature of the DsJ(*) states. We analyze the full set of decays, considering the four lightest DsJ(*) mesons as belonging to the heavy quark spin doublets sℓP=12+ and 32+, with sℓP the spin parity of the light degrees of freedom in mesons. The description implies relations among the observables in various modes. We study the decay distributions in the dilepton invariant mass squared and the distributions in the angle between the charged lepton momentum and the momentum of the produced meson, which are expressed in terms of universal form factors and of effective strong couplings. Such measurements are feasible at present facilities.