SACRAMENTO — A state Department of Motor Vehicles worker slept at least three hours a day on the job for nearly four years, slowing down processing times in an agency known for its long waits, a state audit said Tuesday.

According to the state auditor’s report, the DMV worker napped at her desk for an estimated 2,200 hours of work time between February 2014 and December 2017, costing the state more than $40,000. The employee’s name was not released.

The employee’s supervisors failed to discipline her, despite noting in her performance evaluations that she routinely slept on the job, the audit said.

In response to the audit, the DMV said it could not take disciplinary action against the employee because her behavior had not been properly documented. A warning was issued to the employee in March that she could be disciplined for future on-the-job naps.

Her supervisors were required to complete additional training, the DMV told auditors.

The woman works as a data operator, a position responsible for keying in changes of address and new vehicle ownership forms. On average, auditors said, data operators process 560 documents a day. Their sleepy colleague averaged 200 documents daily, which witnesses told auditors were often error-ridden.

Statewide complaints of extraordinarily long waits at the DMV have prompted California lawmakers to schedule a legislative hearing Aug. 7. While the DMV has long been known for sluggish service, wait times have worsened in recent months in large part because of the Real ID Act, a federal law that requires people to carry special driver’s licenses by 2020 if they want to use them for air travel. That means more people headed to the DMV and more paperwork for DMV staffers.

The DMV began expanding the hours that some offices are open and adding new offices with Saturday hours.

The auditor’s office investigated the DMV employee under the Whistleblower Act and included its findings in its annual report on state worker misconduct.

It was one of 1,481 cases the auditor’s office investigated during the past year.

Among the other cases highlighted:

• A manager at California State University Dominguez Hills approved the purchase of a $7,000 electric vehicle quick-charging station before realizing it would cost $100,000 to install it because it was not compatible with the campus’ electrical infrastructure. The charger has not been used since the university bought it in 2013.

• An employee at Kern Valley State Prison routinely left work 45 minutes early, resulting in 312 hours of missed work time at a cost to the state of nearly $9,000.

• Two groundskeepers at California State University Fresno missed thousands of hours of work between January 2013 and December 2017 by arriving late, taking long breaks and leaving during their shifts for hours. In one day alone, investigators watched as one of the employees missed seven hours of her shift.

Melody Gutierrez is a San Francisco Chronicle staff writer. Email: mgutierrez@sfchronicle.com Twitter: @MelodyGutierrez