His run-ins with the law regarded threats, property damage, fraud and a hit-and-run, but Adomeit said that all charges were dismissed.
Authorities have said the man was a German citizen and that there was "no indication of an Islamist background", but investigators have not said what motivated the attack.
Dramatic pictures showed tables and chairs strewn across a square, leaving six of those injured fighting for their lives in hospital.
Muenster police president Hajo Kuhlisch said the man had four apartments and several cars, all of which were searched by police.
Amri's attack in Berlin in 2016 prompted German lawmakers to call for tougher security measures.
The horrific crash came on the one year anniversary of the Stockholm terror attack in which a hijacked lorry killed five people and seriously injured a dozen more.
"I heard a loud, boring noise and suddenly everyone started shouting", a witness, Steffen Simonsen, told Germany's ARD broadcaster.
"Because of the ongoing investigation, no further information can be given at the present time", the police added in their statement. German news agency dpa says several people killed after auto crashes into crowd in city of Muenster.
North Korea tells U.S. it is prepared to discuss denuclearization
Once a location is agreed upon the officials said that the date will be set and the agenda discussed in greater detail. CNN quoted U.S. officials as saying that the summit will be held in the Mongolian capital Ulaanbaatar.
United Kingdom sugar tax comes into force
How much is the tax? Prices may still rise at some supermarket chains, as The Co-op have confirmed. By all means avoid giving your kids sugar-laden fizzy drinks , but be aware of two things.
Welbeck Bags Brace To Sink Saints
Southampton's defeat kept them in the bottom three, three points behind Crystal Palace but with a game in hand. However, substitute Charlie Austin pulled the Saints level with a tap-in in the 73rd minute.
"This was a disgusting and sad day for the people of Munster, all of Germany. and also the people of the Netherlands, who were sitting here and became victims", he said.
Despite investigators' increased certainty about the perpetrator's mental health, "it will take a few more hours and days" before the case is fully cleared up, North Rhine-Westphalia state interior minister Herbert Reul said on Sunday.
"We are pressing hard on our investigation into all possible avenues".
Police spokesman Bode also said a suspicious object had been found in the vehicle which was being examined.
Local media have identified the man as an industrial designer who had been suffering from psychological problems, but police would not confirm those details.
Munster is a popular tourist destination with 300,000 inhabitants, known for its medieval old town, which was rebuilt after massive destruction during the Second World War.
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.