Probably from the fact that - in past times - when someone died, the blinds in his house and those of his neighbours were drawn down as a sign of mourning. Thus, the notion of something dangling, as it were.
I think it was in the Daily Mirror recently; it refers apparently to King Charles II who was a bit of a ladies man. When he died, women out of respect flashed their petticoats.
I always thought it was a reference to flags being at half-mast. Thanks for reminding us of petticoats which are sadly missed in these days of trouser suits.