Measurements of mass and Λ binding energy of ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$He in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=3$ GeV are presented, with an aim to address the charge symmetry breaking (CSB) problem in hypernuclei systems with atomic number A = 4. The Λ binding energies are measured to be $2.22\pm 0.06$(stat.)±0.14(syst.) MeV and $2.38\pm 0.13$(stat.)±0.12(syst.) MeV for ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$He, respectively. The measured Λ binding-energy difference is $0.16\pm 0.14(\text{stat}.)\pm 0.10(\text{syst}.)$ MeV for ground states. Combined with the γ-ray transition energies, the binding-energy difference for excited states is $-0.16\pm 0.14(\text{stat}.)\pm 0.10(\text{syst}.)$ MeV, which is negative and comparable to the value of the ground states within uncertainties. These new measurements on the Λ binding-energy difference in A = 4 hypernuclei systems are consistent with the theoretical calculations that result in $\mathrm{\Delta }{\mathrm{B}}_{\mathrm{\Lambda }}^4(1_{\text{exc}}^{+})\approx -\mathrm{\Delta }{\text{B}}_{\mathrm{\Lambda }}^4(0_{\text{g.s.}}^{+})<0$ and present a new method for the study of CSB effect using relativistic heavy-ion collisions.