Police had already searched the residence of the 27-year-old Swiss national in eastern Switzerland on Saturday, hours after the deadly attack.
But on Monday Swiss police said he also had a home in the tiny principality of Liechtenstein, which he had reportedly sublet for the past three years.
Police have so far not named the perpetrator, but Swiss media including Blick identified him as Simon S., citing neighbours describing him as tall, lanky and a "loner".
The authorities are working to determine what led the man to carry out the grisly attack on Saturday, on a moving train in the eastern Swiss region of Saint Gallen.
"It is too early to say anything about (the motive)," Saint Gallen police spokesman Gian Andrea Rezzoli told AFP, reiterating that there was no indication it was a terrorist or politically-motivated attack.
He said Swiss police were preparing to study the material retrieved on Sunday in the Liechtenstein search at the man's home.
Both the attacker and a 34-year-old female victim died of their injuries on Sunday.
The deceased has not been officially named but Blick said she was a Croatian national and a divorced mother of two children aged seven and ten.
A friend and neighbour of the woman told the paper said she did not think she knew her killer but was just "in the wrong place at the wrong time."
Police say it remains unclear if the attacker knew any of the victims on the train or if he struck at random.
Several media outlets published a slightly blurry picture allegedly of the attacker with his eyes blacked out, but showing a man with a thin face, blond hair and goatee and apparently wearing steel-rimmed glasses.
"He was a quiet, friendly guy, but I have a feeling he had problems with himself," Blick quoted one acquaintance as saying.
"You could tell he had been teased his whole life," he added, saying the man "had no friends. He was often alone”.
A neighbour meanwhile told 20 Minuten the man "lived in extreme isolation".
The attacker was reportedly the son of a teacher who had worked part-time at a car parts supplier and also attended a technical university in Buchs.