The Midlife Development in the United States Study (2004-06) asked respondents if they have a drinking problem (N = 3,918). Here are the percentages answering yes by religious affiliation:
No religious preference 7.8*
Everyone else 3.6
* significantly higher than "everyone else"
People with no religion are 2-4 times more likely to be alcoholics.
By the way, I thought textbook sociology teaches us that religions that forbid alcohol produce the greatest number of drunks, but only 2.8% of Mormons report this problem.