Brian De Palma's
Sisters
(1973)

Short Version:
There's only one of the siamese twins alive, but with a split personality.

Long Version:
When running out of her medication, "evil twin" Dominique (Margot Kidder) kills the lover of her twin sister Danielle, which is observed by journalist Grace Collier (Jennifer Salt). Danielle's ex-husband Emil (William Finley) comes in and helps hide the body within the couch, and the police finds nothing. Grace finds a cake in the refrigerator with "Dominique & Danielle" written on it, but she slips and falls, destroying the evidence that there were two women.

The paper that Grace works for hires a PI (Charles Durning) to help her. He quickly deduces that the body is in the couch, which is now being transported away to Canada.

Grace finds out that Dominique and Danielle were siamese twins, and that Dominique had died on the operation table when they were separated.

Grace follows Danielle and her ex-husband to the "Linton clinic", a mental institution, and asks to speak with the Chief. However, this is the ex-husband, and he claims that Grace is a new patient, so that she gets "admitted". He puts her under hypnosis and "programs" her to think that there never was a murder. After that, Danielle kills her ex-husband. She gets arrested, and Grace can leave the clinic. However, due to the hypnosis, she insists in a police interview that there never was a murder. The film ends with the PI observing the couch outside a train station in Canada.

Thanks Tilman!