A memorial service was held for victims and their families over the weekend
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Police in Germany say they can find no evidence of a political motive for the van attack in Muenster that left two people dead and 20 injured.
The 48-year-old driver shot and killed himself after hitting diners on a restaurant terrace in a square popular with tourists.
He has been identified and was known to police. The state's interior ministry said he was a loner who suffered mental health problems.
Authorities have searched four homes associated with the suspect, and said they have found "no clues" pointing to an extremist or political motive.
A regional government spokesman said there was no evidence to link the him to any Islamic militant groups and he wasn't a refugee.
According to local media reports a letter was found in his apartment giving details of what were described as humiliating experiences.
People in Munster have been laying flowers and other tributes at the spot where the attack took place.
The visitors of the Kiepenkerl are more down to earth people," said one woman. "Reasonable people. Why do you have to take people's lives? That is incomprehensible to me."
An ecumenical memorial service was held for the victims and their families over the weekend.
"What I've experienced, and those I've talked to are indeed very shocked," said the Auxiliary Bishop of Muenster Dr. Stefan Zekorn. "Many said yesterday, and also today, that it is unimaginable that this is happening here, and that's just how I feel as well."
Eight of the injured people are reported to still be in a life-threatening condition.