Minneapolis Police Chief Tim Dolan expressed "shock and embarrassment" at the allegations but also said other officers in his department helped break the case.
Carson was charged with one count of bank robbery in the holdup at a Wells Fargo bank in Apple Valley one day earlier. He did not respond to the charges at the hearing except to say he understood them, and did not enter a plea.
The motive for the robberies was unclear. But as Magistrate Judge Jeanne Graham appointed a public defender for Carson, she noted a report that said he was carrying "quite a bit of debt."
An affidavit from an FBI agent said Carson admitted robbing the bank, and "admitted having committed numerous other armed robberies" in Dakota and Hennepin counties. It didn't say whether he told investigators why.
FBI spokesman E.K. Wilson said Carson did, but he couldn't comment further.
Carson's public defender, Andrea George, declined to comment on the case. His parents, who were in the courtroom, declined comment after his hearing.
The FBI affidavit said a man wearing a black ski mask, black jacket, blue jeans, dark shoes and black gloves jumped onto the counter at the bank around 9:15 a.m. Wednesday, pointed a gun at all three tellers and demanded all their money. He collected $4,580, put it in a black backpack, and fled. Security video from a nearby Target store showed he ran to a vehicle parked 200 to 300 yards away outside a vacant strip mall.
An Apple Valley police officer helped investigators catch up with Carson, Johnson said.
About half an hour before the robbery, Officer Kurt Schultz stopped Carson's white Mitsubishi Galant three miles away from the bank because it was missing a front license plate, the affidavit said. Carson identified himself as a Minneapolis police officer and told him he had a loaded gun in his car. After checking Carson's police ID and driver's license, Schultz let Carson leave.
Schultz was among the officers dispatched to the bank on the robbery call. On his way there, he spotted Carson's car again, about two miles from the bank.
"He started wondering if this guy was really a Minneapolis police officer, so he started calling Minneapolis," Apple Valley Police Chief Scott Johnson said.
Carson's shift in Minneapolis was scheduled to start Wednesday at 9 a.m., but he arrived about an hour late, the affidavit said.
On Wednesday evening, toward the end of Carson's shift, an Apple Valley detective and an FBI agent went to the Minneapolis Police Department to talk to Carson. The document said he initially denied any involvement in any robberies, but then confessed and told investigators where to find the evidence.
They found some of the black clothing and backpack in a trash can outside the station, the affidavit said, and in his locker they found $2,940 in cash taken from the bank and the gun used in the robbery.
Carson has not been charged in any other robberies so far, but Johnson said Carson "implicated himself" in five other recent armed robberies in Apple Valley, including one at a pharmacy and one of a woman who was making a deposit at the drive-up depository of a U.S. Bank branch.
A Minneapolis police spokesman, Sgt. William Palmer, said Carson is being investigated in four robberies in Minneapolis -- two at gas stations, one at a coffee shop and one at an ATM machine.
Carson became a full-fledged officer in June 2007. The portion of Carson's personnel file released by police showed no disciplinary actions nor any individual commendations.
Dolan told reporters his department spends a tremendous amount of resources trying to recruit the best people.
"We do have a few that fail," he conceded. "It does tarnish the badge."
"It's disgusting," John Delmonico, president of the Minneapolis Police Federation, said of Carson's arrest. "I don't even know what words I could use ... The actions of this guy have a bad reflection on every Minneapolis cop today. For all the cops who go out and do a good job every day, it's pathetic."
Delmonico said the union won't help the accused officer.
