The study of 4,089 families with children answered questionnaires when the child was two months, one and two years old and four years old on environmental factors and symptoms of allergic disease.
Blood was collected from 2,614 children at age four and analysed for immunoglobulin antibodies to common inhalant and food allergens.
Children exposed to tobacco smoke at two months of age are 28% more likely to be sensitive to common inhalant or food allergens, the study found.
Sensitivity was higher for indoor inhaled allergens. Children exposed to smoke are almost twice as likely to be sensitive to cat allergens and 46% more likely to be sensitive to food allergens, the study showed.