So far I see nothing:
http://www.drugs.com/interactions-ch...professional=1

I did see a long post at a spinal board at another forum where a gal said a HEALTH FOOD STORE employee printed out a list of what gabapentin interacts with:
And that list is what sometimes comes up for antiseizure drugs in general...and is not accurate for all of them.

But I will keep looking.

edit: Now this is complex:
http://www.ncbi.nlm.nih.gov/pubmed/18981167
Discusses the carnitine transporter. Gabapentin mentioned but seems to be minor and not significant.

This is a review article.... just a suggestion that some drugs MAY take up the transporter (which is newly defined) in some way and cause deficiency.
http://www.ncbi.nlm.nih.gov/pubmed/22952014

edit--
This paper is about transport across the placenta to a fetus. Gabapentin is mentioned, but not a very potent drug in this specific instance compared to other drugs:
http://www.ncbi.nlm.nih.gov/pubmed/15009220

edit--
This book entry of nutrient depletions as of 2008...discusses the Valproic acid (Depakote) in detail, and lumps all the anti-seizure drugs together:
http://www.ncbi.nlm.nih.gov/pubmed/15009220

Since CMT may be partly or all connected to mitochondrial functions, carnitine may be useful for you for this reason.
You'd have to research that potential separately from the gabapentin etc.