Klumpp, Mialon, and Wiliams have posted this draft on SSRN.  Here is the abstract:

The U.S. Supreme Court has ruled that restrictions on independent political expenditures by corporations and labor unions are unconstitutional on First Amendment grounds (Citizens United v. FEC, 2010). In this paper, we test the hypothesis that the decision gave an electoral boost to Republicans, at the expense of Democrats. The 50 U.S. states provide an ideal testing ground for this hypothesis as the ruling only affected a subset of states. We find that Citizens United had a positive and statistically significant effect of approximately two percentage points on the probability of Republicans winning in state congressional elections.