There is a new NBER paper by Scott Cunningham and Manisha Shah:
Most governments in the world including the United States prohibit prostitution. Given these types of laws rarely change and are fairly uniform across regions, our knowledge about the impact of decriminalizing sex work is largely conjectural. We exploit the fact that a Rhode Island District Court judge unexpectedly decriminalized indoor prostitution in 2003 to provide the first causal estimates of the impact of decriminalization on the composition of the sex market, rape offenses, and sexually transmitted infection outcomes. Not surprisingly, we find that decriminalization increased the size of the indoor market. However, we also find that decriminalization caused both forcible rape offenses and gonorrhea incidence to decline for the overall population. Our synthetic control model finds 824 fewer reported rape offenses (31 percent decrease) and 1,035 fewer cases of female gonorrhea (39 percent decrease) from 2004 to 2009.
Alas, I do not see ungated versions on Google, or maybe try this one (pdf).