Unless you have a contract that protects your job and prevents your employer from requesting that you take the polygraph test you are an employee at will, which means that you can be fired for any reason, except for those legally protected classes (such as race and others). If the employer does not believe you fully cooperated with the investigation then you can be fired. If you consulted an attorney about taking the polygraph I would recommend that you consult your attorney about your termination.
The information that I am providing is general information based on my understanding of your question. You cannot and should not rely on this general advice in making legal decisions. There may be important information that you did not include in your question that could drastically change the advice an attorney that was fully informed would give you. I am not your attorney. My response does not create an attorney client relationship.
You may have rights under the Employee Polygraph Protection Act. Generally, the Act prohibits most private employers from using lie detector tests, either for pre-employment screening or during the course of employment. Employers generally may not require or request any employee or job applicant to take a lie detector test, or discharge, discipline, or discriminate against an employee or job applicant for refusing to take a test. This is the case unless specific exceptions apply. You can learn more about the EPPA and those exceptions at at the Department of Labor website linked below.
I agree with what the others have said, both that you may be protected under the Employee Polygraph Protection Act and that you should consult with your lawyer. For more information on the EPPA, check here: http://www.nolo.com/legal-encyclopedia/state-laws-polygraphs-lie-detector-tests.html. Then again, if you're innocent of the theft and you were warned you would be terminated for not taking the test but continued to refuse to do so, you may have made your own bed on this. Still, if you feel your rights have been violated, the US Department of Labor is who enforces the EPPA. It might be worth calling over there and finding out what your options are.
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