If you’re asking about U.S operator requirements for a Safety Management System, the best answer is; not yet, but you will soon.
Many countries, including Canada (July 2009) already have mandates for a Safety Management System.
The FAA has issued AC 120-92, which introduced the concept of a safety management system to aviation service providers, such as; airlines, air taxi operators, corporate flight departments, and pilot schools. Although the AC is not mandatory and does not constitute a regulation, it does encourage operators to develop and implement a safety management system.
The recent ICOA adopted an amendment to Annex 6 Part II and the new Section III, that applies to jet aircraft and aircraft over 12,500 lbs or 5,700 kgs, introduces the requirement for operations manuals, safety management systems, training programs and fatigue management programs.
However, AC 120-92 states in Appendix 1 that it is in accordance with Annex 6 to the Convention on International Civil Aviation, and the recently mandated International Civil Aviation Organization Document 9859, which is no longer true.
AC 120-92a (amendment to Appendix 1) is in draft and there is no reason to believe that the FAA will not follow with a Notice of Proposed Rule Rulemaking in the near future.