The answer is the EPA. Milady states this directly: "The EPA registers all types of disinfectants sold and used in the United States." That's the same regulatory fact behind the "disinfectants are pesticides" question above — because disinfectants are legally classified as pesticides, the Environmental Protection Agency, not a health or cosmetics regulator, is the one that registers them.
OSHA, the U.S. Department of Labor, and the CDC — the other choices — all play real roles in workplace safety and public health, but disinfectant registration specifically is an EPA function. This is a useful fact to know cold, since it's exactly the kind of specific-agency question that shows up on state board exams.
Milady Standard Barbering, 6th ed., Ch. 4 (Infection Control), p. 60: "The EPA registers all types of disinfectants sold and used in the United States."
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