Even though Lake’s wounds occurred in the line of duty, the policy says his medical leave should be deducted from the overtime.

But three high-ranking police commanders signed off on payroll records showing that Lake was working — even though he wasn’t, sources close to the situation said. They said Lake was asked by the city personnel division to give it back, then told he could keep it.

Lake declined to comment for this story.

He wasn’t the only sergeant affected.

Sgt. Michael Pratt fell Aug. 22 while pursuing an armed suspect, damaging tendons in both legs. Unable to walk for months, he has been off work and may lose his career, said his attorney, Brian Millikan.

The same three supervisors signed off on Pratt’s roughly $2,000 of overtime, but the personnel division discovered it and withheld payment, the sources said.

The St. Louis Police Officers’ Association, which represents sworn employees of the rank of sergeant or below, complains that the way the city applies the policy is unfair and illustrates an imbalance of power between the personnel division and the police department, said its business manager, Jeff Roorda.