WASHINGTON — If your job is protecting the motorcade of the president’s spouse, mouthing off about the boss can lead to more than a citation in a personnel file.

A District of Columbia police officer found that out this week when he came under investigation for threatening comments he was accused of making about Michelle Obama, though there are conflicting reports about what was said, Police Chief Cathy ­Lanier said in an e-mail Friday. She did not elaborate.

Police have not disclosed what the officer, assigned to a unit that provides a motor escort for the White House and other dignitaries, is accused of saying, and it is not clear how seriously the remarks were meant to be taken.

The department and the Secret Service are investigating what a police spokeswoman called ‘‘inappropriate comments.’’

While the Secret Service investigates threats against the first family as a matter of routine, the comments no doubt take on added seriousness given the officer’s role within the department.

The officer has been placed on administrative duty while authorities ­investigate, said Mayor ­Vincent Gray.

The Washington Post cited anonymous police ­officials in reporting that the officer told colleagues he would shoot the president’s wife and then showed a photo on his phone of a gun he would use and that another officer reported the comment to a lieutenant.

D.C. police spokeswoman Gwendolyn Crump has declined to discuss the comments beyond saying that they are under investigation.