From the DHHS regulations:
6. Ask the donor to:

Remove any unnecessary outer clothing (e.g., coat, jacket, hat, etc.)
The donor must not be asked to remove other articles of clothing, (e.g., shirts, pants, dresses, undergarments) or to remove all clothing and wear a hospital or examination gown.
From § 40.61 the DOT regulations:
You must not ask the employee to remove other clothing (e.g., shirts, pants, dresses, underwear), to remove all clothing, or to change into a hospital or examination gown (unless the urine collection is being accomplished simultaneously with a DOT agency-authorized medical examination).

Sources:
Drug Testing
U.S. Department of Transportation / Office of the Secretary of Transportation