This made me curious and figured it would be easy to find where the 3% conviction rate claim comes from and the methodology used.
It is not,in fact I could hardly find anything to support it other than it is a common claim and appears to stem from some UK studies.
The closest thing I found pertaining to the US was this...
http://cmsac.org/facts-and-statistics/Some of those things that are said to be a form of sexual assault are just ludicrous and would mean 100% of the population has been "assaulted".
As far as it goes the best I can deduce is an assumption (I guess based on after the fact claims of rape and not reporting it) that since 50-60% of rapes are not reported then as the justice system works out the rest the conviction rate is inherently going to be low.
As one site I read regarding the same low conviction rate in the UK they noted it is difficult to compare as there is virtually no other crime that such a statistic as been created for...what percent of robbers ever get convicted etc.
I am dubious whenever I see what appears to be an agenda driven statistic and think they do victims a greater disservice then service.