R. perspersa was first described by Edward Meyrick in 1924 using a specimen collected at Otari-Wilton's Bush in Wellington by George Hudson in March.

[2][3] Hudson discussed this species and illustrated the male in his 1928 book The butterflies and moths of New Zealand.

[4] J. S. Dugdale in his 1988 publication Lepidoptera - annotated catalogue, and keys to family-group taxa misspelt the specific epithet as perspera.

[2]Hudson described the female of this species from a specimen collected at Gollan's Valley in February, a month earlier than the holotype.

[4]Hudson goes on to hypothesise that, as a result of the dates of capture, the holotype specimen may be worn or faded.

[7] Under such trees the abandoned cases may be numerous, and indicate that the adult eclosion season is late summer and that the species is univoltine.