Nothing mandatory in statute.
In some industries (especially construction and mining), as a practical matter, if your people are not formally trained, the odds of them not being in violation of OSHA regulations much of the time are pretty slim.
If you are in an unusually-hazardous occupation, and you don't (1) conduct good safety training, and (2) adopt and enforce good safety practices, then when someone gets hurt in a workplace accident, the lack of such training is useful evidence for a Plaintiffs' lawyer. Conversely, proof of such training and policies can serve well as a defensive strategy.
For those who have fixed places of employment (as opposed to jobsites remote from the office or plant), there is often consultation available at little or no cost (a less-known aspect of the Occupational and Safety Act), by which a qualified safety inspector will inspect your premises, and make regimentation so for safe practices, which when complied-with will result in issuance of certification. The certification is actually effective as a "go-away card" if OSHA shows up to conduct an inspection (not effective if the inspection is secondary to an accident with death or injury). Proactive assistance for concerned employers -they're from the government, and they *really are* here to help. And, they are precluded from reporting violations.
In Texas, we call it, "Texas OSHCON."
