Fred Pickel, the city’s ratepayer advocate who analyzes DWP operations, said the department’s high salaries have allowed it to attract good workers.

“You’d expect a work ethic in a group like that,” he said. “Of course, there are always people who abuse.”

The records show one senior accountant averaged 49 extra sick days each year from 2010 to 2012. A security guard averaged 43 extra days. A customer service representative averaged 38 extra days. That’s roughly two months off at full pay, per year, for each of the three employees. It doesn’t include regular sick days, paid vacation days, holidays or “personal” days.

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DWP officials, noting that they were not around when the sick pay policy was adopted in 1981, said they could not find a written rationale for the unlimited extra days. Since 2010, workers have taken 103,802 extra sick days, the equivalent of 415 years.

Here’s how the policy works: The first two days an employee calls in sick are subtracted from his or her allotment of sick days. But if the employee chooses, he or she can take the next eight consecutive work days off, at full pay, without further depleting the sick day supply. No doctor’s note is required for those additional days, which are “on the house,” said one DWP executive who spoke on condition of anonymity because he was not authorized to address the media.

If the employee suffers a relapse of the same illness within 21 days of returning to work, he or she can then take an unlimited number of days off. Again, no days are subtracted from the employee’s sick day supply.

Relapses are supposed to be verified with a doctor’s note, said DWP spokesman Joe Ramallo.

But a department review of 150 employees who took the most extra days off found 67 — fewer than than half — “who appear to have bona fide chronic illnesses, who have doctor’s notes,” Nichols said.

The sick pay data provided to The Times included employees’ job title, the number of extra sick days taken and the amount the employee was paid for those days. The department refused to provide the employees’ names, citing a city attorney’s determination that the records constitute “confidential medical information” and are therefore exempt from disclosure.

Employees across job classifications have taken extra sick days, with the most frequent use among customer service representatives, whose average pay last year was $70,839.

They took 4,632 extra days in 2012 and were paid $1.3 million for that time.

About 35% of them took no extra days, but the remainder averaged 11 extra days off.