If you refuse the test they can terminate you without any legal recourse. In fact, since you most likely do not have a contract of employment, and are thus an "employee at-will," your employer can fire you for any reason without legal recourse - other than unlawful discrimination. It is not uncommon when there is employment theft involved for the employer to request a polygraph test. You can refuse the test, of course, but if they terminate you because of that refusal you will have no cause of action to sue them.
The Employee Polygraph Protection Act provides limitations on the employer's right to require you to submit to a polygraph examination. Generally, if the employer does not have reaonable suspicion that you were involved in the theft, you cannot be compelled to submit to the examination and you cannot be discharged for refusing. You can vist the Department of Labor website to obtain more detailed information regarding your rights under the Act.
The Employee Polygraph Protection Act (EPPA) generally prohibits lie detector tests, including polygraph tests, by private employers. There are some exceptions, one is called the "ongoing investigation" exception. It would appear that that is available here, since money is missing. However, before an employer can claim protection under this exception, it must comply with strict requirements in the EPPA. Preliminarily, it must show (1) that it has an economic loss, (2) that the employee had access to the property, and (3) that the employer has reasonable suspicion that the employee WAS [ not may be] involved in the loss. Moreover, even if an employer can satisfy these three things, it still has to follow strict procedures before, during, and after the polygraph test. If an employer fails to follow one of the EPPA procedures, and there are many, then it no longer can justify the test under the "ongoing investigation" exception, and the test would be illegal under the EPPA. Here , you state that the employer did not give written notice, which is one of the EPPA requirements. The written notice, moreover, must be very specific and tell you, among other things, what the economic loss is, what access you had to the property, and the basis, in detail, of the reasonable suspicion that the employer has that you were involved in the loss. Also, the employer here is asking all managers to take a polygraph which may mean that it is engaging in what is called a "fishing expedition". If so, that would also be illegal under the EPPA.