After the employee is offered the position the Employer may ask questions about disabilities, including questions about Worker's Compensation if they ask the same questions of all the applicants for that job type. The same rule applies for medical examinations. If this is not a general consistence practice then medical information cannot be queried unless there is a direct threat or a proven business necessity.
From EEOC Guide:
After I got a job offer, the employer had me take a medical examination in which I revealed I have epilepsy. Can the employer withdraw my job offer?
While the employer had the right to require a post-offer medical examination, he cannot withdraw the job offer solely because you revealed you have a disability. Instead, the employer can withdraw the job offer only if it can show that you are unable to perform the essential functions of the job (with or without reasonable accommodation), or that you pose a significant risk of causing substantial harm to yourself or others.
Example: Darla receives a job offer to be a cook at a hotel resort, and during the medical examination she discloses that she has epilepsy. The hotel doctor expresses concern about Darla working around stoves and using sharp utensils. Darla tells the doctor that her seizures are controlled with medication and offers to bring information from her neurologist to answer the doctor's concerns. Darla also points out that she has worked as a cook for seven years without any incidents. The hotel will violate the ADA if it withdraws Darla's job offer based on her epilepsy.
What are examples of questions that an employer cannot ask on an application or during an interview?
Examples of prohibited questions during the pre-offer period include:
• Do you have a heart condition? Do you have asthma or any other difficulties breathing?
• Do you have a disability which would interfere with your ability to perform the job?
• How many days were you sick last year?
• Have you ever filed for workers' compensation? Have you ever been injured on the job?
• Have you ever been treated for mental health problems?
• What prescription drugs are you currently taking?
May the employer ask me these questions after making a job offer?
Yes. An employer can ask all of the questions listed above and others that are likely to reveal the existence of a disability, after it extends you a job offer as long as it asks the same questions of other applicants offered the same type of job. In other words, an employer cannot ask such questions only of those who have obvious disabilities. Similarly, an employer may require a medical examination after making a job offer as long as it requires the same medical examination of other applicants offered the same type of job.