Simple answer: No. Employers cannot require that employees take a polygraph test, but if the employee voluntarily agrees to take the test, and the employer makes certain disclosures to the employee, then the employer may administer a polygraph.

California Labor Code section 432.2 is the governing labor code section. It states:

432.2. (a) No employer shall demand or require any applicant for employment or prospective employment or any employee to submit to or take a polygraph, lie detector or similar test or examination as a condition of employment or continued employment. The prohibition of this section does not apply to the federal government or any agency thereof or the state government or any agency or local subdivision thereof, including, but not limited to, counties, cities and
counties, cities, districts, authorities, and agencies. 

(b) No employer shall request any person to take such a test, or administer such a test, without first advising the person in writing at the time the test is to be administered of the rights guaranteed by this section.

Therefore, employers may administer polygraph tests if the employees voluntarily agree to the test and are informed of their rights under Labor Code section 432.2. Employers need to be careful, however, as federal law may also apply. It also raises a difficult issue for the employer: What if the employee refuses to take the test? Under section 432.2 the employer cannot use this refusal to take the test as grounds to terminate the employee. If there is a termination, the employee would likely argue that it violated his or her rights under this section, and this would leave the employer in a difficult position in explaining why the termination occurred.