Although I've mentioned biotin (vitamin B7) in the context of autism before on this blog (see here), due credit needs to be given to Peter over at the Epiphany blog for more extensive coverage (peer-reviewed based) of this nutrient (see here). Discussing how, within the increasingly large range of conditions that manifest autism or autistic behaviour(s), there may be one or two 'types' of autism that manifest biotin deficiency, there is a pretty obvious course of intervention as and when deficiency is found: supplementation.
And supplementation is exactly what was discussed in the paper by Paul Benke and colleagues  reporting on a case report of a young female who presented with "features of autism spectrum disorder, isolated headaches, and episodes of headaches and limb shaking." Alongside those symptoms, authors also discussed a fairly unusual part of her clinical history where "hair and nails did not grow."
Although there are various reasons why hair and nails might not grow - indeed, just about every nutritional deficiency seems to affect something like nail health and growth - biotin was noted as a point of concern in this young lady's clinical picture. Indeed authors noted that: "Administration of biotin restored her nail and hair growth and improved intellectual ability and school performance." They added that use of acetazolamide, more typically indicated for glaucoma and/or epilepsy, seemed to provide some relief from other symptoms: "episodes of headaches, single limb shaking, and loss of consciousness." And before you say it, yes, autism is no protection against the development of headaches (see here).
Bearing in mind this was a single case report yet also acknowledging the tenet: 'if you've met one person, you've met one autistic person', I find descriptions such as this to often be revealing. Other case reports talking about biotinidase deficiency associated with autism , where biotinidase is the enzyme responsible for freeing up biotin bound to food (see here), add to the interest in this area. Specifically how some other symptoms - "seizures, weak muscle tone (hypotonia), breathing problems, hearing and vision loss, problems with movement and balance (ataxia), skin rashes, hair loss (alopecia), and a fungal infection called candidiasis" - associated with biotinidase deficiency are not a million miles away from what has been talked about in some autism literature too (see also the comments section of another post here).
As per my discussions on various other nutrients that seem to be 'deficient' in at least some people on the autism spectrum (see here and see here), the defining message seems to be that post-diagnosis of autism, a screening program needs to be put into place looking at various nutrients in the context of something like eating patterns and behaviours. This could be part of a broader range of screening for something like inborn errors of metabolism that can and do show a connection to some autism (see here) and often (always?) involve nutrients (see here for example). Or could just mirror what is happening in other parts of psychiatry, where physiological parameters are starting to gain some parity with behavioural/developmental/psychiatric ones (see here) mindful of what correcting any deficiency might bring to various aspects of health (see here)...
 Benke PJ. et al. Biotin and Acetazolamide for Treatment of an Unusual Child With Autism Plus Lack of Nail and Hair Growth. Pediatr Neurol. 2018 Feb;79:61-64.
 Zaffanello M. et al. A case of partial biotinidase deficiency associated with autism. Child Neuropsychol. 2003 Sep;9(3):184-8.