You could probably do this relatively easily in R with GenomicRanges. Read in the RefSeq track, convert the transcripts to GRanges and then apply a function that computes the distance between a range and the output from nearest().

Edit: Here's an example:

library("GenomicRanges")
refGene <- read.delim("~/Downloads/refGene.txt", header=T)
gr <- GRanges(seqnames=Rle(refGene$chrom), 
    ranges=IRanges(start=refGene$txStart, end=refGene$txEnd, names=refGene$name),
    strand=Rle(strand(refGene$strand))) 
neighbors <- nearest(gr) #This can return NA
REMOVE <- whichis.na(neighbors))
neighbors <- neighbors[-REMOVE]
neighbor <- gr[neighbors]
gr <- gr[-REMOVE]
distances <- distance(gr, neighbor)

I just tried this on my laptop and it seems to work fine. If this isn't exactly what you want, you should be able to easily modify it.