"This large study showed a prospective association of infant muscle tone with autistic traits in childhood."
So said the findings reported by Fadila Serdarevic and colleagues  who, looking at nearly 3000 children, were able to assess early motor development and muscle tone "between ages 2 and 5 months" and later parental ratings of autistic traits in children at 6 years of age. Said autistic traits were surveyed using the "the Social Responsiveness Scale (SRS) and the Pervasive Developmental Problems (PDP) subscale of the Child Behavior Checklist." Authors concluded that there was something of a connection between low muscle tone and autistic traits: "Low muscle tone in infancy predicted autistic traits measured by SRS... and PDP" and further: "early detection of low muscle tone might be a gateway to improve early diagnosis of ASD [autism spectrum disorder]."
Just before anyone gets ahead of themselves with this data, it is worth pointing out that despite the large participant group included for study and the prospective nature of the study design, this was a study only really looking at two sets of variables across quite a long time-frame. It's not beyond the realms of possibility that other factors might influence the presentation of [parent-reported] autistic traits outside of just early measures of muscle tone or anything related...
But let's set this research in some context. Muscle tone in a broader sense had been noted to be potentially 'linked' to autism in some of the earliest texts on the topic (see here). More recent discussions on how motor skill in the context of gait for example, might be something important to at least some autism (see here) add to the relevance. One might also look to the some of the typical reasons why low muscle tone (hypotonia) may present to see whether there are areas that could inform autism research too. I note for example, mention of Ehlers-Danlos syndrome (EDS) in some of the texts and this would perhaps appeal to further investigation on any overlap between EDS (or other connective tissues disorders) and autism (see here). Serious infections such as encephalitis and meningitis have also been mentioned in the context of hypotonia, and again, might be indicated in relation to hypotonia and some autism (see here). There is also a possibility that hypotonia could (in some cases) be tied into mitochondrial disease; something else that could be relevant to at least some 'types' of autism (see here). All of these areas are worthy of further research inspection added to the idea that muscle tone might be rather more core to autism than many people might appreciate.
'And the best picture goes to'...
 Serdarevic F. et al. Infant muscle tone and childhood autistic traits: A longitudinal study in the general population. Autism Res. 2017 Feb 9.
Serdarevic F, Ghassabian A, van Batenburg-Eddes T, White T, Blanken LM, Jaddoe VW, Verhulst FC, & Tiemeier H (2017). Infant muscle tone and childhood autistic traits: A longitudinal study in the general population. Autism research : official journal of the International Society for Autism Research PMID: 28181411