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That was a key conclusion reported in the study by Hilda Razzaghi and colleagues  based on their analysis of data from "the 1997-2011 National Health Interview Survey", a US initiative which aims to provide "information on the health of the U.S. civilian noninstitutionalized population through confidential interviews conducted in households" (see here).
I have to say that I was pretty interested in these findings (even though this is not the first time that neurodevelopmental outcomes have been tied to CHD); a view it seems, that was shared by the authors of the paper, bearing in mind the very wide confidence intervals (CIs) detailed for both conditions and the reliance on second-hand reporting over actual independent screening results. I can't readily offer any one 'smoking gun' explanation for the findings specifically in relation to the autism spectrum but will draw your attention to some discussion about the potential causes of congenital heart disease provided by the NHS Choices websites and how they might tie in.
So: various genetic conditions including Down's syndrome are linked to CHD  and the net seems to be closing in on some of the underlying genetics around the association . Although still in need of quite a bit more study, there is a growing appreciation that a diagnosis of autism / autistic traits can coexist alongside a diagnosis of Down's syndrome (see here). As per a recent conversation (thanks Marilyn), one also wonders how this autism - Down's syndrome link might also play out with regards to other areas of the autism research landscape such as dietary effects for example...
Next up is maternal diabetes. As per the NHS Choices entry: "It is estimated that 3 to 6% of women with diabetes who become pregnant will give birth to a baby with a heart defect". Autism and maternal diabetes is an interesting topic which has again cropped up in the autism research literature . If you want my take on the Xu meta-analysis paper and related literature, look no further...
After that is a role for alcohol consumption during pregnancy and mention of the condition called foetal alcohol syndrome (FAS). I have talked about FAS and foetal alcohol spectrum disorder (FASD) before on this blog in the context of autism (see here) but can't readily conclude that the links are overly strong between FAS/FASD and autism presentation.
"A rubella infection can cause multiple birth defects, including congenital heart disease". An interesting association given the history of rubella and autism based to quite a large extent on the work from Stella Chess . I don't know enough about the rate of rubella infection in pregnant women to make any informed statement about how this risk factor might tie into both CHD and autism but the numbers of non-immune women do seem to be quite alarming here in the UK .
Influenza during pregnancy? "Women who get flu during the first trimester (three months) of pregnancy are twice as likely to give birth to a baby with congenital heart disease than the general population" according to the NHS Choices website. Regular readers of this blog might already know that I tend to talk quite a bit about how infection - immune system response to infection - during pregnancy seems to have some link to subsequent offspring psychology and development (see here). The link is not altogether straight forward with autism in mind and potentially better related to concepts like fever or fever control  but still, there might be more to do here.
The final links - certain medications taken during pregnancy, phenylketonuria (PKU) and exposure to organic solvents during pregnancy - have also, to various extents, been linked to autism (see here and see here for example).
I may very well just be plucking at straws trying to link the causes of CHD with some of the suspected 'causes' of autism (some autism at least) but it strikes me that if one was to further pursue the findings reported by Razzaghi et al those would be the places to start (assuming some shared effect). As per the reports of other physiological findings potentially manifesting alongside a diagnosis of autism (see here), some additional screening of children on the autism spectrum where one or more of the correlates of CHD are suspected might be indicated.
Peter Gabriel and Kate Bush with a beautiful song to close: Don't Give Up.
 Razzaghi H. et al. Long Term Outcomes in Children with Congenital Heart Disease: National Health Interview Survey. J Pediatr. 2014 Oct 8. pii: S0022-3476(14)00820-8.
 Laursen HB. Congenital heart disease in Down's syndrome. Br Heart J. Jan 1976; 38(1): 32–38.
 Ramachandran D. et al. Contribution of copy-number variation to Down syndrome-associated atrioventricular septal defects. Genet Med. 2014 Oct 23. doi: 10.1038/gim.2014.144.
 Xu G. et al. Maternal diabetes and the risk of autism spectrum disorders in the offspring: a systematic review and meta-analysis. J Autism Dev Disord. 2014 Apr;44(4):766-75.
 Chess S. Follow-up report on autism in congenital rubella. J Autism Child Schizophr. 1977 Mar;7(1):69-81.
 Skidmore S. et al. Is the MMR vaccination programme failing to protect women against rubella infection? Epidemiol Infect. 2014 May;142(5):1114-7.
 Zerbo O. et al. Is maternal influenza or fever during pregnancy associated with autism or developmental delays? Results from the CHARGE (CHildhood Autism Risks from Genetics and Environment) study. J Autism Dev Disord. 2013 Jan;43(1):25-33.
Razzaghi H, Oster M, & Reefhuis J (2014). Long Term Outcomes in Children with Congenital Heart Disease: National Health Interview Survey. The Journal of pediatrics PMID: 25304924