The promoter of Charlie Sheen’s national stage-show tour paid D.C. police $445 to cover the cost of the high-speed police escort that the actor was given Tuesday night as he hurried to DAR Constitution Hall, the department said.

How the escort was arranged has yet to be explained, however, and Police Chief Cathy L. Lanier said Friday that the apparently improper use of police resources remains under investigation by the department’s internal affairs division.

“Our written policy states that police vehicles shall be used for escort duty only for the purpose of providing security for the president and vice president of the United States and such visiting heads of state or their representatives who may require extra-ordinary protective measures,” the chief said in a statement Friday.

She said, “It appears our protocols ... were not followed in this instance.”

Sheen and his handlers — traveling in two sport-utility vehicles with a police car in front and another behind— were running late for the scheduled 8 p.m. start of Sheen’s show after they landed in a private jet Tuesday night at Dulles International Airport.

A photo taken in one of the SUVs and posted to Sheen’s Twitter account shows the vehicle’s speedometer needle at 80 mph as the motorcade headed to Washington.

Police spokeswoman Gwendolyn Crump the promoter, Live Nation Worldwide, wrote a $445.68 check to the D.C. Treasurer, dated Tuesday.