This is a great question but very difficult to answer given the fact that Montresor committed a perfect crime: no one apparently saw Montresor and Fortunato together; when they get to Montresor's palazzo, all the servants are gone, so there are no witnesses who can connect Montresor and Fortunato at the palazzo; there is no apparent motive because Montresor has completely hidden his anger over the insult; and, most important, there is no body.
Assuming, however, that someone saw the two together, perhaps on the way to Montresor's palazzo or entering the palazzo, a prosecutor of the time would be aware of Montresor's catacombs, and as soon as it was obvious that there was nothing in the palazzo itself to indicate a possible crime, a good prosecutor would want to examine the catacombs.
Once in the catacombs, the prosecutor would simply follow any available evidence, in this case, the wine bottles from which Montresor and Fortunato drank as they descended to the lowest levels. In that time, fingerprint technology didn't exist, so the prosecutor would only be able to conjecture that one or more persons had been recently drinking from the empty wine bottles. Because the catacombs were probably dusty, there might be footprints to follow--and because Fortunato was dressed as a jester, his shoes might have left distinctive prints.
When the prosecutor arrives at the lowest level where Fortunato was walled up, Montresor might have left some evidence of his actions, not thinking that anyone could have traced him to that point. Based on either evidence of materials left around or the realization that part of the wall appears newly made, the prosecutor might have a chance at discovering the body, which would have been critical in charging Montresor with the crime.