Carrolla was named for the type species by Langston & Olson (1986) for a single, complete skull collected from the early
Permian of Archer County, Texas; the specimen is reposited at the
Texas Memorial Museum in Austin. They immediately recognized the similarity to '
Brachystelechus,' the eponymous genus from Europe; this genus was subsequently synonymized with
Batropetes, traditionally considered a reptile but which had taxonomic precedent. Numerous features were cited as evidence for an ability to burrow, which was considered rare among 'microsaurs' at the time, and several shared features with modern
amphibians were noted, although some of these have been subsequently disproven. Maddin et al. (2011) provided a detailed re-description of the holotype based on
CT data; this study was one of the first to explore 'microsaur' anatomy using tomographic methods. These authors provided substantial new information on the internal anatomy, particularly the braincase, and recovered support for close affinities of brachystelechids and
caecilians in the longstanding debate over the origin of modern amphibians. Mann et al. (2019) reported the first postcrania of the taxon based on a small block that was catalogued with the holotype skull but never described; the authors indicate that correspondence with K.W. Craddock, who found the holotype, corroborates that the postcrania block was recovered in association with the skull. The authors also validated Glienke's (2015) previous cursory interpretation of at least some of the teeth as tricuspid, a feature found in some other brachystelechids. == Anatomy ==