Is an Arc Flash Study Legally Required?
The short answer: OSHA doesn't name "arc flash study" directly, but its general requirements make one practically unavoidable for most commercial and industrial facilities.
What OSHA Requires
OSHA's general duty clause and specific electrical safety regulations (29 CFR 1910 Subpart S) require employers to protect workers from electrical hazards, including arc flash. OSHA does not mandate a specific study format, but it does require employers to determine hazards and provide appropriate PPE — which in practice means you need some form of hazard analysis.
Where NFPA 70E Comes In
NFPA 70E is a consensus standard, not a law — but OSHA recognizes it as an accepted way to demonstrate compliance with the general duty clause. Courts and OSHA inspectors routinely treat NFPA 70E as the de facto standard of care. This is why nearly every facility with exposed energized equipment ends up getting a study done, even though no single law says "you must have an arc flash study."
Practical Bottom Line
If your facility has employees who work on or near energized electrical equipment above a minimal voltage/current threshold, you should assume you need a documented hazard analysis — and an arc flash study is the standard, defensible way to produce one.