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Creutzer comments on Open Thread, February 1-14, 2013 - Less Wrong
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You're quite right that it'd be very hard to demonstrate a causal effect (and without having read the study itself - don't have access -, I suspect the researchers didn't even want to try).
Actually, I have no idea how that could be done in practice. For voluntary hospitalization, it would be helpful if one couldn't be hospitalized against one's will, but I'm not aware of a time and place where that would be the case, and don't expect there to be any. So one can study that only outside the realm of "hospitalization-worthy" suicidality, by using patients who have been offered hospitalization, but declined it, as a control. My quick search turned up no indication of even that having been done.
And for forced hospitalization, it seems sort of impossible in principle to find a control group...
I also just found this, again I don't have access, and unfortunately it doesn't even have an abstract. Might be relevant, though, judging by the title.
Check for that first link on Pubmed. I was able to access the article that way.
I'm not finding this new article anywhere. The text in a Google book search where the study had been mentioned suggests that it's probably not the type of study I'm looking for though.
I doubt this type of study exists. About the best we could do is to compare the suicide rate in an area with no legal method for hospitalizing suicidal people against their will (if that exists and the country is developed enough to keep such statistics reasonably well) with the suicide rate of a comparable area.