That was the conclusion reached by Ryosuke Asano and colleagues  based on their analysis of data derived from the Hamamatsu Birth Cohort (HBC) Study . The idea being that the more subtle presentation of issues linked to a diagnosis of autism spectrum disorder (the BAP) might predispose to a great likelihood of other behavioural or psychiatric symptoms  to be present. We'll see about that.
|What're you lookin' at, ya hockey puck?|
The Asano paper is open-access but just in case...
- As part of the HBC study looking at pregnant women to ascertain "an early diagnostic algorithm for [offspring] ASD"  researchers garnered various snippets of information from over 800 pregnant women in mainland Japan.
- Covering mid-pregnancy to approximately 3 months after childbirth, women were asked to complete the Edinburgh Postnatal Depression Scale (EPDS) (a tool fairly routinely used here in the UK) to "measure their depressive symptoms after childbirth". The EPDS was completed 3 times after childbirth (between 2-4 weeks, 5-7 weeks and 8-12 weeks).
- The BAP was assessed using the Broader Phenotype Autism Symptoms Scale (BPASS)  and administered via interview "mainly during the 2nd trimester of the pregnancy". Authors also did some additional work to "check whether our use of the BPASS is reliable and valid". Potential confounders such as a history of depression or anxiety and the level of emotional support provided by partners during pregnancy were also examined in participants; indeed, some 11% of the research cohort "had a history of depression and/or anxiety disorders".
- Results: "The overall cumulative incidence of PPD was 15.2%". This figure is not a million miles away from other estimates of PPD  based on the use of the EPDS (albeit with a slightly different cut-off point). Indeed, the HBC study had already hinted at something around this figure previously .
- Scores on the BAP were "weakly but positively associated with depressive symptoms after childbirth at all measurement periods". I have to say that despite these various correlations being significant, I was not particularly impressed with the correlation (r) values reported (ranging from 0.14 to 0.16 assuming 0 is no correlation and 1 is a perfect correlation). Indeed, when looking at the mean (average) composite score of the BPASS (see Table 1) between the PPD and non-PPD groups you can see there is very little difference in measured BAP (13.77 vs. 13.14).
- Again, based on the data provided in Table 1, of more interest is the effect of a history of depression/anxiety on PPD status, where 30/128 (23%) and 65/713 (9%) of the PPD and non-PPD groups respectively reported. The authors note that a: "history of depression and/or anxiety disorders was associated with a more than 3-fold increase in the risk of PPD".
With all due respect to the authors, I have to say that I'm not convinced that scoring high on the BAP is truly a major risk factor for postpartum depression. I'm not totally ruling out any relationship as per the Ingersoll findings on the BAP and depressed mood  or based on the increasing body of work looking at autism and subsequent mood disorders (see here for example). It's just that there are far more likely predictors/predisposers to PPD than subclinical autistic traits. Indeed, yet another paper from the HBC study  further hinted at some of those other factors based on that history of depression/anxiety among other things.
Music then... You've got the love (Florence + The Machine version).
 Asano R. et al. Broader autism phenotype as a risk factor for postpartum depression: Hamamatsu Birth Cohort (HBC) Study. Research in Autism Spectrum Disorders. 2014; 8: 1672–1678.
 Tsuchiya KJ. et al. Searching for very early precursors of autism spectrum disorders: the Hamamatsu Birth Cohort for Mothers and Children (HBC). Journal of Developmental Origins of Health and Disease. 2010; 1: 158-173.
 Ingersoll B. et al. Increased rates of depressed mood in mothers of children with ASD associated with the presence of the broader autism phenotype. Autism Res. 2011 Apr;4(2):143-8.
 Verreault N. et al. Rates and risk factors associated with depressive symptoms during pregnancy and with postpartum onset. J Psychosom Obstet Gynaecol. 2014 Sep;35(3):84-91.
 Matsumoto K. et al. Age-specific 3-month cumulative incidence of postpartum depression: the Hamamatsu Birth Cohort (HBC) Study. J Affect Disord. 2011 Oct;133(3):607-10.
 Mori T. et al. Psychosocial risk factors for postpartum depression and their relation to timing of onset: the Hamamatsu Birth Cohort (HBC) Study. J Affect Disord. 2011 Dec;135(1-3):341-6.
Asano, R., Tsuchiya, K., Takei, N., Harada, T., Kugizaki, Y., Nakahara, R., Nakayasu, C., Okumura, A., Suzuki, Y., Takagai, S., & Mori, N. (2014). Broader autism phenotype as a risk factor for postpartum depression: Hamamatsu Birth Cohort (HBC) Study Research in Autism Spectrum Disorders, 8 (12), 1672-1678 DOI: 10.1016/j.rasd.2014.08.010