Within the math absorption band of CH₂BrCl, we theoretically analyze the laser-induced control of the Br/Cl branching ratio, Br + CH₂Cl ← CH₂BrCl → CH₂Br + Cl, with CH₂BrCl initially in its vibrational ground state. For weak-field excitation, the Br/Cl branching ratio increases as a function of wavelength, however, for wavelengths below 180 nm the branching ratio cannot be made smaller than 0.4. Using optimal control theory, we show that the branching ratio can be made significantly less than 0.4, only when very strong fields are employed. Thus, the present work strongly suggests that a Tannor-Rice type laser control mechanism for selective bond breakage in CH₂BrCl cannot take place without accompanying photoionization.