Not directly, as OSHA (Occupational Safety and Health Administration) does not approve or certify products. What OSHA does do is set forth standards for testing, use, and safety features. They visit work places and do inspections, review accident reports and can potentially fine worksites for violations if OSHA recommendations are not met. OSHA guidelines on ladders are found under Standard Number 1926.1053 and can be viewed here.
The standards that OSHA follows are developed by two non-government organizations, ALI and ANSI. The American Ladder Institute (ALI) is a nonprofit organization that promotes safe ladder use. It is "the approved developer of ladder safety standards" for the American National Standard Institute (ANSI). ANSI, also not-for-profit, sets standards for nearly every industry, and ensures that US products remain competitive in the global market. ANSI requirements may be more substantial than OSHA specifications, particularly if the industry decides that additional testing should be done.