Citing officials who spoke on condition of anonymity, The Washington Post reported Thursday the police department Internal Affairs Division is investigating the matter and has notified the Secret Service.
D.C. police spokeswoman Gwendolyn Crump told the newspaper in an e-mail the department has "received an allegation that inappropriate comments were made. We are currently investigating the nature of those comments."
The officer in question has worked as a motorcycle escort for White House officials. He was assigned to administrative duty Wednesday, the Post reported.
The newspaper's police department sources said the officer -- whose name has not been reported -- allegedly made the threatening comments Wednesday during a discussion among officers from the Special Operations Division concerning threats against the Obamas. The officials said the officer told them he would shoot the first lady, and then pulled up a picture on his phone he said was the weapon he would use.
In an e-mail, a Secret Service spokesman told the Post the agency was aware of the matter and would "conduct appropriate follow-up."
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