Police stressed on Monday that the attack was not terror-related.
As the manhunt continued, the insurance company said it was keeping its offices in Schaffhausen and five other nearby towns closed for now "in view of yesterday's attack".
Police have said they believe Wrousis specifically targeted CSS, and was a customer of the company.
A police official said Wrousis had previous weapon offences dating back to 2014 and 2016.
Schaffhausen, a town of about 36,000 people north of Zurich, is near the Swiss-German border.
However, police did say the life of the man most seriously injured is no longer threatened. They said they had identified the attacker, but did not name him, describing him in a statement appealing for help from the public as bald, unkempt and around six feet three inches tall.
Authorities had issued an worldwide arrest warrant for Wrousis, whom they described as aggressive and psychologically unstable.
The attack began in an insurance office, Sticher said, and a Volkswagen van that belongs to Wrousis has been found.
Armed police stand guard at the scene of the attack in central Schaffhausen.
The suspect's vehicle, a white Volkswagen, has been found but he remains on the run and is presumed risky, although not necessarily armed, ATS said, quoting police.
Therese Karrer, who often walks her dog in woods south of Schaffhausen, said she saw the suspect several times in the last few weeks. They did not elaborate on its condition or say if anything else was found in it.
"I talked to him a few times and walked by his vehicle every day with our dog", said Karrer, who lives in the village of Uhwiesen.
A shop owner told Swiss newspaper Blick a man with a chainsaw was walking the streets and police later confirmed the report.
There were, however, different accounts as to how the deceased, identified as Tunde Azeez, 27, from Osun State was killed. Trouble, it was gathered, started Wednesday morning when a mobile policeman shot the trailer driver.
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