By Kathy Finn

NEW ORLEANS (Reuters) - Jury deliberations may begin on Thursday in the federal perjury trial of two New Orleans police officers accused of lying about the killing of a civilian in the aftermath of Hurricane Katrina in 2005.

The trial is among the final judicial steps in the city's effort to put behind it multiple charges of police misconduct in the wake of the country's worst natural disaster.

Ronald Mitchell and Ray Jones do not dispute shooting Danny Brumfield Sr. in September 2005, and lawyers for the police officers have sought to highlight inconsistencies in eyewitness accounts about the circumstances.

Mitchell and Jones are charged with giving false testimony and obstructing justice during a federal wrongful death lawsuit filed by Brumfield's widow against the city of New Orleans. They each face up to 20 years in prison if convicted.

The officers were driving a patrol car past the city's convention center where throngs of people went to seek food and shelter after fleeing flooded homes when they encountered Brumfield.

The officers contend Brumfield lunged at them with "a shiny object" in his hand, prompting Mitchell to shoot him with a pistol-grip shotgun.

But Brumfield's brother-in-law testified Wednesday that when Brumfield waved his arms to flag down the cops, the police car sped up and he jumped onto the car's hood to save himself.

David Augustin said he was several feet away when he saw a "flame" from the gunfire, and saw Brumfield fall to the street, where the car proceeded to run over him.

"The car never stopped," Augustin said.

The case is the latest to stem from a U.S. Justice Department probe into possible police misconduct in the immediate aftermath of Katrina, when many parts of the city remained under several feet of water.

In March 2011, the U.S. Justice Department released a scathing report on the New Orleans Police Department, itemizing dozens of areas in which police were lax or showed outright disregard for public safety and protection.

The federal government is expected eventually to impose a legal decree on New Orleans requiring the police department to address the shortcomings identified in the report.

Federal prosecutors launched multiple investigations into possible civil rights violations by police that occurred both before and after Katrina struck the city.

In the largest case, a jury last summer convicted five officers on 25 counts in connection with the September 2005 fatal shooting of two unarmed civilians, the wounding of four others and a cover-up of the crimes that went on for more than four years.

(Editing by David Bailey and Greg McCune)