In one scene, Peter Venkman says that the place the Ghostbusters are at could "scare Stephen King." Stephen King is a noted fan of H.P. Lovecraft, whose mythos features heavily in this episode. He has even written a short story, "Jerusalem's Lot," that borrows heavily from the Lovecraft mythos.
Several characters are named after authors from the "Lovecraft Circle" including Ted Klein (named after T.E.D. Klein), Clark Ashton (named after Clark Ashton Smith), Alice Derleth (named after August Derleth), and Mr. Howard (named after Robert E. Howard).
The voice actors were recorded on July 30, 1986.
The title on the episode call sheet was "The Collect Call of Cthulhu".
Cathulhu received an entry in the 2016 tie-in book "Tobin's Spirit Guide - Official Ghostbusters Edition" on page 70 and 71, where it's Class is listed as unclassifiable.