I haven't come across any studies. If there was one, it would need to be controlled for known biases, such as refs attempting to even the number of fouls called on each team, calling more fouls on the team in the lead, and calling more fouls on the road team.
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This study examines the pattern of foul calls exhibited during 365 NCAA basketball games during the 2004-2005 season. Results of the analysis indicate that officials are more likely to call fouls on the team with the fewest fouls, making it likely that the number of fouls will tend to even out during the game. This increased probability increases as the foul differential increases. In addition, there is a significant bias toward officials calling more fouls on the visiting team, and a bias toward foul calls on the team that is leading in score. The result is that the probability of the next foul being called on the visiting team can reach as high as .70 during some game circumstances.
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http://home.kelley.iupui.edu/kyjande...%20version.pdf