The line strength ratios for the R and P branches (the rotational branching ratios) are measured for the first time for the GK ¹Σ⁺ _g, v′, J′ → B ¹Σ⁺ _u, v″, J″ spontaneous transitions of the H₂ molecule. Values of 73 branching ratios for 18 different (v′-v″) bands with the rotational quantum numbers J′ = 1-9 and vibrational quantum numbers v′ = 0-3 and v″ = 0-7 are obtained. Significant discrepancies (exceeding a factor of 20-30) are found between the experimental data and the results of calculation in the adiabatic approximation using the Hönl-London factors and taking into account the effect of vibrational-rotational interaction in the vibrational wave functions of combining states. These perturbations are more significant than those observed in our previous work for transitions from levels of both the triplet 3p complex of terms and the singlet and triplet 3d complexes of terms of the hydrogen molecule. It was established that the effects of perturbation in the rotational branching ratios strongly depend not only on values of J′ for separate vibronic bands, but also on values of v′ and v″ for fixed values of J′.