At Empirical Legal Studies blog, Bill Henderson summarized (scroll to third entry) an unfortunately linkless paper on the subject presented at the ALEA [American Law and Economics Association] conference:

Ronen Avraham & Max Schanzenbach, "An Empirical Study of the Impact of Tort Reforms on Health Insurance Coverage," which was a very clever time-series analysis that showed a relation between tort reform legislation and higher rates of insurance coverage (i.e. fewer uninsured). Although the effect is not large, it does corroborate the idea that fewer successful lawsuits = less defensive medicine = lower insurance costs = more people with insurance.