Can you dust for fletching?

Maybe it's because I'm reading a mystery and writing something science-fictiony right now, but this sounds like the beginning of a very weird plot. A woman in the Bronx was hit by an arrow as she opened the passenger door of her car to let a friend out at a nursing home. The story is written to play up the bafflement, and probably the answer is simple–some 12-year-old boy coming up with a not-too-bright idea and running away–but until a prosaic solution arrives, this seems like something out of a novel I'd want to read.