Strangers on a Train [suggested by Phil Howarth]

The psychologists would call it folie a deux…

‘Bruno slammed his palms together. ‘Hey! Cheeses, what an idea! I kill your wife and you kill my father! We meet on a train, see, and nobody knows we know each other! Perfect alibis! Catch?”

From this moment, almost against his conscious will, Guy Haines is trapped in a nightmare of shared guilt and an insidious merging of personalities.who are at once bound together and separated by forces beyond their control. [product description from Amazon]

The book has a Wikipedia entry, and was famously made into a film, released in 1951 and directed by Alfred Hitchcock, which has its own page.

Author’s Wikipedia page.