Christian Schlögl et al. have published "A Comparison of Citations, Downloads And Readership Data for an Information Systems Journal" in a special issue on altmetrics of Research Trends.
Here's an excerpt:
In our analysis we identified a high (though not a perfect) correlation between citations and downloads which was slightly lower between downloads and readership frequencies and again between citations and readership counts. This is mainly due to the fact that the used data (sources) are related either to research or at least to teaching in higher education institutions.