At the Oxford Practical Ethics blog, Matt Baum objects to cities that have bike rental programs but don’t provide helmets to riders. His conclusion:

I applaud these city-transport schemes for being innovatively convenient and environmentally friendly. But the city, if it is going to provide such a scheme, has a responsibility to make it possible to (and indeed encourage people to) use it safely. In this case, the city has a responsibility to provide helmets.

To be sure, there’s a tension here between public health officials’ campaigns to increase rates of helmet use and local governments renting bikes to people without providing helmets. But I don’t think this is ethically such a big deal, because there’s a lot of evidence that bike helmets don’t do much to make bike riding safer.

Western Australia enacted a mandatory bike helmet law in 1992, causing helmet use rates to rise from 37% to 82%. Here’s a graph with the results:

Head injuries didn’t obviously decrease all that much, while upper limb fractures rose a lot. Risk compensation could explain why increased helmet use may not have the beneficial effect that its proponents hoped for: people who wear helmets feel safer and thus are less careful when they are riding.

Here is a study reporting results that “are consistent with the notion that those who use helmets routinely perceive reduced risk when wearing a helmet, and compensate by cycling faster.” This study found that automobile drivers are less careful around helmet-wearing cyclists than they are around bare-headed cyclists.

There are other studies that showing that helmet use does decrease head injuries (here is one), but based on my cursory examination of the literature, it doesn’t seem like there’s good enough evidence that bike helmets make cyclists safer to justify legislation mandating them. And the evidence definitely is sufficiently inconclusive to exonerate governments of cities with non-helmet providing bike share programs from any moral culpability.