I found the methodology here.
The measure is 'Well-being', not happiness. It averages six scores:
•Life Evaluation
•Emotional Health
•Physical Health
•Healthy Behavior
•Work Environment
•Basic Access
1/4 of the score for healthy behavior is 'smoking' and the study is 'self-report'.
A rough estimate is that 4.2 points of the final score depend on the proportion of the population who report smoking. the US average is 21% while Utah is at 9%. So Utah gets about a .5 point advantage on the smoking question alone.
Then the self-report option brings it's own problems - for example half (about 8points of the final score) of the Life Evaluation is where you think you will be in 5 years time. I would hazard a guess that LDS may be more 'optimistic' on that front, having been promised material blessings for paying tithing. As noted earlier there is only 8 points between top & bottom states.
The biggest problem with the media report is that the study measures well-being, not happiness at all. And a number of the wellbeing items directly relate to wealth and tolerance (respect), so the results are not too surprising overall.