There's a section on these weapons in Donn Draeger's book on classical bujutsu, which unfortunately I don't have with me at the moment. There were actually three weapons, the third being a catchpole similar to that used in Europe, and they were used by squads of three constables. After the shogunate was instituted, they became symbols of justice, and were displayed by magistrates at trials and punishments..
According to what I remember from Draeger, the reason that these poles were used was not because the constables couldn't touch the samurai, but rather because, during the Warring States Period (which is when these were used), the samurai were so dangerous that, to catch one alive (say, after a drunken brawl), a squad of three people with these implements was necessary. It's similar to medieval Europe, where the town constables used catchpoles of similar design for much the same reason.
Draeger wasn't fond of Tokugawa-era martial arts. He thought that they had deteriorated from the standard of the Warring States Period. One of his bits of evidence was that, during the Warring States period, the constables needed sleeve entanglers and worked in squads to catch samurai, whereas during the Tokugawa regime, they used staves, chains, and jitte (similar to sai) to catch samurai, and often worked alone. Something to think about.
My 0.02 cents,
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