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RANGEL’S SICK JOKE

There’s nothing like a tragic police shooting to bring a tasteless guffaw out of Rep. Charlie Rangel.

Speaking yesterday at a rally in honor of slain cop Omar Edwards — gunned down by a fellow cop in a case of mistaken identity — the embattled congressman outrageously quipped that President Obama, in town for a date with First Lady Michelle, should watch his back walking around the Big Apple because he is black.

“Make certain he doesn’t run around East Harlem unidentified,” the controversial lawmaker snarked.

“If [he] did not have the Secret Service . . . around him, [city cops] wouldn’t know if he was president of the United States.”

The remark brought raucous cheers and laughter from the crowd of around 100.

Police union officials were quick to blast Rangel’s remarks.

“If Congressman Rangel said . . . ‘and waving a gun’ he might be correct,” the union official said.

But Rangel wasn’t the only official riffing on the fact that Edwards, who is black, was shot by a white officer.

“First we couldn’t ‘drive while black,’ now we can’t ‘police while black,’ ” said Brooklyn City Councilman Charles Barron.

Mayor Bloomberg, who stopped by the Edwards’ Brownsville home to pay his respects to the family, said a federal investigation into the shooting wasn’t necessary despite calls from activists.

But Gov. Paterson, however, left open the door to outside involvement.

“I think that the NYPD and the Manhattan DA are perfectly capable of conducting the investigation, but I think in these types of situations, what is most important is that everybody is satisfied,” he said.

Meanwhile, Edwards’ widow bravely fought back tears yesterday as a parade of officers carried her husband’s personal items from his car into her Brooklyn home, including his prized football.

“When his wife saw it, she started crying. There was a football. That was his passion — football,” said Eugenio Edwards, an uncle of the officer tragically gunned down by a fellow member of the Finest in East Harlem on Thursday night.

Danielle Edwards, 22, had just endured a sleepless night and was feeling a little more composed until Omar’s grim-faced colleagues showed up.

They had cleaned out Edwards’ Nissan — which a petty thug had burglarized, setting off the grim chain of events — and wanted her to have his possessions.

Most sentimental was the football. Edwards, a father of two, had been a player since high school and was a defensive back on the NYPD team, which is set to face off against the FDNY team today.

His son, Xavier, 18 months, already seems to understand something is amiss.

“I’m worried about him. His father would come home from work, hold him and play with him,” Eugenio said.

Omar’s heartbroken father, Ricardo, last night defended his son’s split-second actions.

“My son is a hero no matter what anyone else says,” he said. Edwards is due to receive an inspector’s funeral with full departmental honors.

Additional reporting by John Doyle, Christina Carrega, Matthew Nestel and Angela Montefinise