The 17-page study also found that 67 percent of the respondents know that their companies have privacy policies that affect their customers, even when the companies were not doing a good job of communicating such policies to their employees.

Asked whether more government regulations are needed to help protect worker privacy, 46 percent of the respondents said yes, while 37 percent said no. "People want more rights, but they don't necessarily think a new regulation is going to help them," Ponemon said. Instead, improved compliance from employers is needed rather than new laws, according to the survey results. "People are against more regulation, but that doesn't mean that they don't want their employers to do a better job."

The top five categories that workers want their employers to safeguard are sexual orientation, credit reports, performance histories, Social Security numbers and health records, according to the study.

In addition, 57 percent of respondents said that it would take only one data breach incident by their company involving their personal data for them to lose confidence in the company's ability to protect their information.