In another case, a truck engine was cranked without the clutch being pressed, and it moved forward and struck a person working under the hood. The person was knocked to the ground but not hurt, according to the documents.
The investigation was opened May 19, according to documents posted by the agency on Friday. An investigation can lead to a recall, but so far none has been issued.
Chrysler said in a statement that it is cooperating in the investigation. The company said that customers with concerns about their trucks should contact their dealer.