I was curious if a certain mechanoreceptor in the skin may be involved in this sensitivity. And indeed, there has been some research done on this question. From what I've seen, researchers are linking hyper/hypo-sensitivity to touch in ASD to the Lamellar corpuscles. These are the mechanoreceptors that detect vibrations in the 250 Hz range.
Here are the sources that I found which discuss it.
"Autism spectrum disorder in the scope of tactile processing"
Mark Mikkelsen, Ericka L. Wodka, Stewart H. Mostofsky, Nicolaas A. J. Puts
Developmental Cognitive Neuroscience - Volume 29, January 2018, pages 140-150
"In this review, we focus on tactile processing dysfunction in ASD."
"Blakemore et al. (2006) investigated detection threshold for both flutter (30 Hz) and vibration (200 Hz) stimulation in adults with Asperger syndrome (AS) and found that adults with AS had significantly lower detection thresholds for the 200-Hz stimulus. No differences were found for flutter stimulation, although a trend was apparent. This suggests that adults with AS were less sensitive to flutter stimulation, hinting that over-responsiveness in AS is specific for vibration but not flutter." Blakemore et al - S.J. Blakemore, T. Tavassoli, S. Calo, R.M. Thomas, C. Catmur, et al. "Tactile sensitivity in Asperger syndrome", Brain Cognit., 61 (2006), pp. 5-13
"These studies suggest that while light touch processing remains intact in ASD, dynamic processing of vibrotactile stimuli might be altered in ASD. The differences and cross-modulation between vibration and flutter are unclear, indicating possible differences between RAI and Pacinian channels or in higher-order processing."
"Vibration Perception Thresholds in Children With Idiopathic Toe Walking Gait"
Cylie M. Williams, BAppSc, MHlthSc; Paul Tinley, PhD; Michael Curtin, BOccThy, MPhil, EdD; ...
Journal of Child Neurology - March 20, 2012
"This study investigated the vibration perception differences between children with an idiopathic toe walking gait and their non–toe walking peers... A highly significant difference in the vibration perception threshold between the groups was determined. The idiopathic toe walking group demonstrated a lower vibration perception threshold (P = .001), indicating this group was highly sensitive to vibration input..."
"Sensory Processing in Autism: A Review of Neurophysiologic Findings"
Elysa Jill Marco, Leighton Barett Nicholas Hinkley, S S Hill, and Srikantan Subramanian Nagarajan
Pediatric Research - 2011, May; 69 (5 Pt 2) 48R-54R
"The psychophysical tactile studies look at thresholds and sensitivity using vibrotactile stimuli. Adults with AS showed lower tactile perceptual thresholds for 200Hz but not 30Hz vibrotactile stimuli, implying a specific hypersensitivity in the Pacinian corpuscles receptor pathway (3). Tactile hypersensitivity was again shown to vibrotactile stimuli as well as thermal stimuli but not to light touch in adults with autism (26)."
3. Blakemore SJ, Tavassoli T, Calo S, Thomas RM, Catmur C, Frith U, Haggard P. Tactile sensitivity in Asperger syndrome. Brain Cogn. 2006;61:5–13.
26. Cascio C, McGlone F, Folger S, Tannan V, Baranek G, Pelphrey KA, Essick G. Tactile perception in adults with autism: a multidimensional psychophysical study. J Autism Dev Disord. 2008;38:127–137.