U.S. Department of Labor Occupational Safety and Health Administration
What are employers required to provide concerning medical examinations?
In construction and shipyards, you must provide medical examinations for workers who, for 30 or more days per year, engage in Class I, II, or III work or experience exposure above a PEL.
In general industry, you must provide medical examinations for workers who are exposed above a PEL.
Courtesy of U.S. Department of Labor Occupational Safety and Health Administration

The OSHA standards for permissible asbestos exposure limits