Your state does not have a statute which restricts polygraph testing but there are guidelines that the employer must follow. Before a polygraph can be administered the employer must give the employee written notice 48 hours prior to any testing, stating that the employee is a suspect. There must also be provable, reasonable suspision that the employee is involed in the theft or other misconduct that triggered the investigation (so they can't just round up all the employees on the shift and make them all take the test). There needs to be some proof that your daughter might be involved before they can ask her to take the test (not just "well she is on the same shift that money keeps disappearing from").
The employer MUST then read to you (the employee, and mother can sit in on all meetings about the polygraph and the polygraph itself if the child is a minor) and ask you to sign a statement that includes:
1. A list of topics you cannot be asked, including questions on religious beliefs, sexual preference, racial matters, lawful activities of labor organizations and political affiliation.
2. The information that you have the right to refuse to take the test.
3. The fact that you cannot be required to take the test as a condition of your employment (this is what you may want to look for).
4. An explanation on how the test works.
5. An explanation of your legal rights if the test is not given in keeping with the law.
While the test is being administered, you have the right:
1. To stop at any time.
2. To be asked questions in a way that is not "degrading or needlessly intrusive."
If the test is not done to these specifications the agency you must file a complaint with is the U.S. Department of Labor.