There is virtually no fossil record for the Copepoda. A few odd examples were found in lake deposits in North and South America (Palmer, 1969) with high levels of boron. Also a parasitic example was found on the gills of a lower Cretaceous fish (Cressy and Patterson, 1973).
Cressy, R. and C. Patterson. 1973. Fossil parasitic copepods from a Lower Cretaceous fish. Science. 180: 1203-1285.
Palmer, A. R. 1969. Copepoda. In: Treatise on Invertebrate Paleontology. Part R. Arthropoda. 4(1). R. C. Moore ed. Geol. Soc. Am. and Univ. Kansas Press, Lawrence. R200-203 pp.