The electric E1 and magnetic M1 dipole responses of the N= Z nucleus ²⁴ Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the ²⁴ Mg(γ, γ^′) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one J^π= 1 ^- , four J^π= 1 ⁺ , and six J^π= 2 ⁺ states in ²⁴ Mg. De-excitation γ rays were detected using the four high-purity germanium detectors of the γ ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total B(M1)↑=2.7(3)μN2 is observed, but this N= Z nucleus exhibits only marginal E1 strength of less than ∑ B(E1) ↑ ≤ 0.61 × 10 ^{- 3} e 2 fm ² . The B(Π1,1iπ→21+)/B(Π1,1iπ→0gs+) branching ratios in combination with the expected results from the Alaga rules demonstrate that K is a good approximative quantum number for ²⁴ Mg. The use of the known ρ2(E0,02+→0gs+) strength and the measured B(M1,1+→02+)/B(M1,1+→0gs+) branching ratio of the 10.712 MeV 1 ⁺ level allows, in a two-state mixing model, an extraction of the difference Δβ22 between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV 02+ level.