The City Morgue is a frequent location visited by the main cast in their constant investigations of murders. The Coroner allows Emerson Cod and his associates access to the dead bodies, in exchange for some monetary compensation. This agreement was made after the Coroner began to get suspicious of how many different kinds of "expert" Ned was pretending to be. Bryan Fuller has also said in interviews that the Coroner is personally attracted to Emerson.
From the outside, the building looks several stories tall, but few rooms have been seen other than the Coroner's Office, and the main room which bodies are stored in. The facility does seem short on space, as the same room was used to store all of the bodies from a drowned clown car at once.