Legal Question in Business Law in New York

In general, yes an employer can ask an employee, or prospective employee, to take a drug test at any time. The employee can refuse to take the test, but the employer can also choose not to hire them or keep them on the payroll. If the employer is a government institution or receives government funding they will have many more rules to follow regarding when, how, and what recourse they can take if you refuse or fail the test. If you are a member of a union there may be specific procedures they would need to follow as well and you should speak with your union representative.