I agree with Chuck. If you don't agree to the test they could simply terminate you, guilty or not. What are you worried about, their questions will be about the money only, nothing about personal life.
They must comply wiith the Employee Polygraph Protection Act of 1988 (http://www.law.cornell.edu/uscode/text/29/chapter-22).
In particular, they must comply with 29 USC § 2006 (d). (http://www.law.cornell.edu/uscode/text/29/2006)
"(d) Limited exemption for ongoing investigations
Subject to sections 2007 and 2009 of this title, this chapter shall not prohibit an employer from requesting an employee to submit to a polygraph test if—
(1)the test is administered in connection with an ongoing investigation involving economic loss or injury to the employer’s business, such as theft, embezzlement, misappropriation, or an act of unlawful industrial espionage or sabotage;
(2)the employee had access to the property that is the subject of the investigation;
(3)the employer has a reasonable suspicion that the employee was involved in the incident or activity under investigation; and
(4)the employer executes a statement, provided to the examinee before the test, that—
(A)sets forth with particularity the specific incident or activity being investigated and the basis for testing particular employees,
(B)is signed by a person (other than a polygraph examiner) authorized to legally bind the employer,
(C)is retained by the employer for at least 3 years, and
(D)contains at a minimum—
(i)an identification of the specific economic loss or injury to the business of the employer,
(ii)a statement indicating that the employee had access to the property that is the subject of the investigation, and
(iii)a statement describing the basis of the employer’s reasonable suspicion that the employee was involved in the incident or activity under investigation. "