The coroner takes care of the bodies of many of the people that Ned, unbeknownst to him, resurrects in order to solve their murders and earn the reward money. The coroner has expressed a degree of suspicion regarding Ned on multiple occasions, but also seems apathetic to Ned's true intentions as long as he himself gets paid.
The coroner first encountered Ned and Emerson Cod, Ned's partner in his crime solving scheme, when they wanted to investigate the body of Leo Gaswint, a man who was apparently murdered by his dog. The coroner let the men investigate the body, even though he voiced suspicion at Ned's claims that he was a "dog expert" since a dog expert had already visited the morgue. 
The coroner later voiced suspicion again when Ned, Emerson and Charlotte "Chuck" Charles asked to investigate the corpse of Matthew Miltenberger. When he asked whether Ned was the dog expert who previously visited the morgue, Ned simply said that he was not. The coroner obviously did not believe him, but let him investigate the body anyway. 
He became even more suspicious when Ned, Emerson, and Chuck came to investigate the body of Bernard Slaybeck. This time Ned said that he, Emerson, and Chuck were from the Government Safety Place, but he said it as if he was asking a question. The coroner once again just gave his "mmmm hmmmmm" and let them through. 
Personality and traits
The coroner is a sleepy-eyed man with a mustache and beard. He is suspicious of Ned and Emerson's visits to the morgue, which he voices with a quiet, "Mmm hmm." Despite this, the coroner has never tried to interfere with their investigations, nor has he pried into the secret of Ned's touch or shown any signs of being aware of it.  He has a vast knowledge of hand moisturizer.