WASHINGTON — The stunt had all the trappings of a high school prank: cheeky if innocuous intentions, a lack of foresight and authority figures called in at the end to deal with the antics.

But on Thursday, the mischief maker in question was the House Republican campaign arm, and the prank — delivering empty cardboard moving boxes to Democratic lawmakers topped with bows and bearing the handwritten message “Get Packing!” — prompted the United States Capitol Police to investigate.

The cartons arrived in offices on Capitol Hill not long after the House voted, almost entirely along party lines, to lay out rules for the impeachment inquiry into President Trump.

Democrats pushed the measure through the House over unanimous Republican opposition, a move that Republicans fervently hope can be weaponized against Democrats in the coming elections. It is yet another way, they believe, to target the most politically vulnerable Democrats in conservative-leaning districts, by painting them as beholden to the party’s left flank and preoccupied with removing the president.