The study compared children in a low income area in NYC to a similar group in New Jersey, which doesn't have menu labelling requirements. It found that there was no significant difference in caloric purchasing between the two groups.
Of course this is only one study and it needs to be replicated in different contexts. It adds to the existing evidence suggesting that menu labelling won't be the simple policy solution to population obesity rates that some might hope.
Read the study, or some coverage of its findings. Also revisit the related HIA that was conducted in LA County and the excellent Robert Wood Johnson review on Menu Labeling: Does Providing Nutrition Information at the Point of Purchase Affect Consumer Behavior?