Once you have been hired and started work, your employer cannot require that you take a medical examination or ask questions about your disability unless they are related to your job and necessary for the conduct of your employer's business. Your employer may conduct voluntary medical examinations that are part of an employee health program, and may provide medical information required by State workers' compensation laws to the agencies that administer such laws.
UPDATE: Since writing this post in August 2017, several important changes have taken place in the laws regarding ADA compliance for websites. On December 26, 2017, the Department of Justice announced that they have withdrawn the Obama-era Advance Notice of Proposed Rulemaking mentioned in this article which intended to require ADA website compliance. The DOJ’s withdrawal announcement stated, “The Department will continue to assess whether specific technical standards are necessary and appropriate to assist covered entities with complying with the ADA.”
The ADA states that a "covered entity" shall not discriminate against "a qualified individual with a disability".[12] This applies to job application procedures, hiring, advancement and discharge of employees, job training, and other terms, conditions, and privileges of employment. "Covered entities" include employers with 15 or more employees, as well as employment agencies, labor organizations, and joint labor-management committees.[13] There are strict limitations on when a covered entity can ask job applicants or employees disability-related questions or require them to undergo medical examination, and all medical information must be kept confidential.[14][15]
The ADA states that a "covered entity" shall not discriminate against "a qualified individual with a disability".[12] This applies to job application procedures, hiring, advancement and discharge of employees, job training, and other terms, conditions, and privileges of employment. "Covered entities" include employers with 15 or more employees, as well as employment agencies, labor organizations, and joint labor-management committees.[13] There are strict limitations on when a covered entity can ask job applicants or employees disability-related questions or require them to undergo medical examination, and all medical information must be kept confidential.[14][15]
Any business that is considered a “place of public accommodation” is required to provide equal access to services under the nondiscrimination requirements of Title III of ADA. When you look at the guidelines closely, this includes hotels, entertainment venues, legal and accounting firms, retail stores, and virtually every business that is not a private club, including businesses that exist solely on the web.
Reasonable accommodation is any change or adjustment to a job or work environment that permits a qualified applicant or employee with a disability to participate in the job application process, to perform the essential functions of a job, or to enjoy benefits and privileges of employment equal to those enjoyed by employees without disabilities. For example, reasonable accommodation may include:

In an August 2016 case involving the University of California Berkeley, the DOJ ruled that the public university was in violation of ADA Title II (similar to Title III but it instead applies to government organizations) because their YouTube channel’s videos didn’t include captions for hearing impaired visitors. The DOJ found this to violate the ADA as deaf users did not have equal access to the online content.
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”
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