In a study by Yuksel, et al. (2008), children with moderate asthma had significantly higher scores than non-asthmatic children on the Conners’ Parent Rating Scale-48 (CPRS), an ADHD rating scale. 

A study by Blackman & Gurka (2007) also found that children with asthma had a higher rate of ADHD.  As severity of asthma symptoms increased, so did the rate of ADHD symptoms. 

There may be a few reasons behind these findings.  There may be shared genes for asthma and ADHD.  In addition, some medications for asthma can cause side effects similar to ADHD symptoms.  Also, when you can’t breathe, you have increased anxiety (I have asthma and there’s something about lacking air that makes you a little panicked), and some symptoms of anxiety can mimic symptoms of ADHD.  There is also the possibility that ADHD and asthma are inherited independently of one another, with one disorder not actually increasing the likelihood of developing the other.  And there is always a possibility that the reason is a combination of the factors above, or other factors. 

Yuksel, H., Sogut, A., & Yilmaz, O.  Attention deficit and hyperactivity symptoms in children with asthma.  Children with more severe asthma symptoms had more severe ADHD symptoms.  The Journal of Asthma, 45(7), 545-547.

Blackman, J.A. & Gurka, M.J. (2007).  Developmental and behavioral comorbidities of asthma in children.  Journal of Developmental and Behavioral Pediatrics, 28(2), 92-99.