Two people were killed and several more were injured in Muenster Saturday when a 48-year-man drove a van into a crowd before committing suicide.
About 20 people were injured in the incident, six seriously, which occurred near the Kiepenkerl statue in the city's old town area.
He was shot dead by Italian police in Milan four days later while on the run.
Amri's attack in Berlin in 2016 prompted German lawmakers to call for tougher security measures.
Muenster's Roman Catholic bishop is urging mourners to try to understand - with the help of God - the frightful van crash that killed two people and injured 20 others.
Witnesses of Saturday's crash had initially said they'd seen two other perpetrators flee the van after it crashed into a crowd outside the city's traditional Kiepenkerl pub in the city's medieval old town.
Broadcaster ZDF said police were searching his apartment and that he had contact with far-right extremists, but there was no evidence thus far that he was a far-right extremist himself.
Armin Laschet, the governor of North Rhine-Westphalia state where Munster is located, toured the city on Sunday.
YouTube shooter was calm in interview before attack
The entire family was "very, very friendly", according to Rundell, who spoke most often with the father, an electrical contractor. But her brother said he expressed additional concern upon learning she was discovered by police so close to the YouTube campus.
The incident comes at a time of a heightened concern in Europe, following a spate of jihadist attacks using vehicles to kill pedestrians in the UK, France and Sweden. "The investigations are being conducted at full speed and on all fronts", he added.
He said, "People are calm, but really shocked", adding that people were scared and disbelieving that such an attack could happen in Muenster.
"So far there are no indications of a possible background for the crime", senior public prosecutor Martin Botzenhardt said in a joint statement with Muenster police. It showed pictures of where police had cordoned off an area of the city. "The investigations are being led under high pressure in all possible directions".
Local media have identified the man as an industrial designer who had been suffering psychological problems, but police would not confirm the details.
Police spokesman Bode also said a suspicious object had been found in the vehicle which was being examined.
Police during a search found a weapon - a Kalashnikov.
Lino Baldi, who owns an Italian restaurant near the scene of the crash, told Sky TG24 that the city center had been packed with people out enjoying a Saturday market and summer-like temperatures, which had risen to 25 degrees Celsius (77 degrees Fahrenheit) from just 12 degrees (54 degrees F) a day earlier.