The scientists say that even exposure to low levels of tobacco smoke can be detrimental to behaviour.
"These findings should encourage us to make stronger efforts to prevent childhood exposure to tobacco smoke, especially among higher risk populations, such as children with asthma," said Dr. Kimberly Yolton, lead author of the study and a researcher at the Children's Environmental Health Center at Cincinnati Children's.
The researchers also observed during the study that girls, though exposed to higher levels of tobacco smoke than boys on average, did not shown an increase in behavioural problems.
However, behavioural problems increased about two fold in boys, with each doubling their tobacco smoke exposure.
The researchers said that further studies were required to find out why there were different degrees of behavioural impact among the 220 boys and girls, ages 6-12, in the study.
"The largest increase we observed was in overall behavioural problems, but it was interesting that in addition to externalising behaviours - like hyperactivity and aggression - we also saw an increase in internalising behaviours, such as depression. Few studies have found a link between tobacco smoke and depression in children," said Dr. Yolton.
An article on the study has been published in the Journal of Developmental and Behavioral Pediatrics.