From part(s) 1 and 2.
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Crossing the border into Iowa, they take refuge from a rainstorm in an empty barn, where they find and steal a 1956 Chevrolet. The Kansas City police, meanwhile, have identified the stolen Chevrolet, which has been traced to the fugitives. Sightings of the car allow police to have an idea of their movements.
Dick and Perry "finding" the car story is important because later on in the book, we learn that there was a murder in Tallahassee of a family. That's significant because that family was going to buy the same car that Dick and Perry "found". Which leads readers to wonder if Perry's story is true... did they really "find" the car in the barn , or did they kill the family as everyone suspects and that's where the car truly came from?