Silence of the Lambs was a horror film. It was known to involve particularly extreme crimes.
After a manhunt began with Dr. William Secare being hunted by police for a moving violation before going missing beneath the seawater in Ardis harbor, Captain Roy Lacerio referenced Silence of the Lambs while he was questioned by FBI Special Agents Fox Mulder and Dana Scully. He admitted hunting a man for a moving violation was not exactly as extreme as Silence of the Lambs but that it was one of the actions typically carried out by the police. (TXF: "The Erlenmeyer Flask")
This work of fiction is actually entitled The Silence of the Lambs, though has consistently been referred to as Silence of the Lambs in episodes of The X-Files. The film version of the story was based on a novel by Thomas Harris and features Hannibal Lecter, who is referred to as "Hannibal the Cannibal" in TXF: "The Jersey Devil".
The Silence of the Lambs was one of the major influences in the creation of The X-Files, with clear parallels between Dana Scully and the film character of Clarice Starling. Series creator Chris Carter acknowledged, "I was a big fan of that film, and I think that actually was as great an influence as anything on the show." (The Complete X-Files: Behind the Series, the Myths and the Movies, p. 28) For instance, the release of the film, set in an FBI context, helped push the idea of using the FBI as a natural means of entry into investigations of paranormal phenomena such as the ones reported in the X-files. (The Truth Is Out There: The Official Guide to The X-Files, p. 11)
Glen Morgan observed that the pilot episode of The X-Files partly mirrored The Silence of the Lambs. Comparisons with Clarice Starling's investigation in the film can easily be found in the episode "Beyond the Sea", which Morgan co-wrote; there was even a reluctance on Fox's part to produce that episode because of the similarity. Morgan responded, "If people say it's derivative of Silence of the Lambs, that's just a brilliant idea Thomas Harris came up with." (X-Files Confidential, pp. 36, 59 & 60)
A scene where Clarice Starling consults her entomologist friends Roden and Pilcher for help about a chrysalis found in a victim's throat is clearly evocative of Mulder and Scully's numerous visits to the Lone Gunmen; Roden physically resembles a young Melvin Frohike and sounds like Richard Langly in voice and tone. This scene brings comic relief to an otherwise dark film through light-hearted dialogue and humorous close-up shots; similar shots of the Lone Gunmen inspecting evidence abound throughout The X-Files and The Lone Gunmen television series.
Additionally, The Silence of the Lambs is mimicked in a scene from The X-Files' final episode, "The Truth", when an imprisoned Mulder momentarily jokingly assumes the role of Hannibal Lecter and directly refers to Scully as "Clarice". He specifically says, "I smelled you coming, Clarice," which may be a reference to the fact Hannibal Lecter, upon initially meeting Clarice Starling when she first visits his prison cell, says, "I can smell your cunt."