Can my employer ask about my disability after they have made me a job offer?

Yes. Guidance from the Equal Employment Opportunity Commission offers this guidance. Once an employee is on the job, his/her actual performance is the best measure of ability to do the job. When a need arises to question the ability of an employee to do the essential functions of his/her job or to question whether the employee can do the job without posing a direct threat due to a medical condition, it may be job-related and consistent with business necessity for an employer to make disability-related inquiries or require a medical examination.