In the city where the “defund the police” movement took off, voters will decide next week whether to replace their Police Department with a new public safety agency.MINNEAPOLIS — Days after a police officer murdered George Floyd, protesters gathered outside Mayor Jacob Frey’s home demanding that the Minneapolis Police Department be abolished. The mayor said no. The crowd responded with jeers of “Shame!”On Tuesday, nearly a year and a half since Mr. Floyd’s death thrust Minneapolis into the center of a fervent debate over how to prevent police abuse, voters in the city will have a choice: Should the Minneapolis Police Department be replaced with a Department of Public Safety? And should Mr. Frey, who led the city when Mr. Floyd was killed and parts of Minneapolis burned, keep his job?Minneapolis became a symbol of all that was wrong with American policing, and voters now have the option to move further than any other large city in rethinking what law enforcement should look like. But in a place still reeling from the murder of Mr. Floyd and the unrest that followed, residents are deeply divided over what to do next, revealing just how hard it is to change policing even when most everyone agrees there is a problem.“We’re now known worldwide as the city that murdered George Floyd and then followed that up by tear-gassing folks who were mourning,” said Sheila Nezhad, who decided to run for mayor after working as a street medic during the demonstrations, and who supports the proposal to replace the Police Department. “The message of passing the amendment is this isn’t about just good cops or bad cops. This is about creating safety by changing the entire system.”Sheila Nezhad decided to run for mayor after working as a street medic during the demonstrations after George Floyd was murdered by the police.Caroline Yang for The New York TimesMany residents have a dim view of the Minneapolis Police Department, which before Mr. Floyd’s death had made national headlines for the 2015 killing of Jamar Clark and the 2017 killing of Justine Ruszczyk. In recent weeks, a Minneapolis officer was charged with manslaughter after a deadly high-speed chase and, in a separate case, body camera video emerged showing officers making racist remarks and seeming to celebrate hitting protesters with nonlethal rounds. A poll by local media outlets last month found that 33 percent of residents had favorable opinions of the police while 53 percent had unfavorable views.Despite those misgivings, the overwhelmingly Democratic city is split over how to move forward. Many progressive Democrats and activists are pushing to reinvent the government’s entire approach to safety, while moderate Democrats and Republicans who are worried about increases in crime say they want to invest in policing and improve the current system. In the same poll last month, 49 percent of residents favored the ballot measure, which would replace the Police Department with a Department of Public Safety, while about 41 percent did not.The divisions extend to the top of the Democratic power structure in Minnesota. Representative Ilhan Omar and Keith Ellison, the state attorney general, support replacing the Police Department. Their fellow Democrats in the Senate, Amy Klobuchar and Tina Smith, oppose it, as does Mayor Frey.Police officers along Lake Street in Minneapolis during protests last year.Victor J. Blue for The New York Times“I know to my core that we have problems,” said Mr. Frey, who said his message of improving but not defunding the police had resonated with many Black voters, but not with white activists. “I also know to my core that we need police officers.”Since Mr. Floyd’s killing, many large cities, Minneapolis included, have invested more money in mental health services and experimented with dispatching social workers instead of armed officers to some emergency calls. Some departments scaled back minor traffic stops and arrests. And several cities cut police budgets amid the national call to defund, though some have since restored funding in response to rising gun violence and shifting politics.In the days after Mr. Floyd’s death, as protests erupted across the country, Minneapolis became the center of a push among progressive activists to defund or abolish the police. A veto-proof majority of the City Council quickly pledged to disband the Police Department. But that initial effort to get rid of the police force sputtered, and “defund the police” became a political attack line for Republicans.If the ballot measure passes next week, there would soon be no Minneapolis Police Department. The agency that would replace it would focus on a public health response to safety, with more City Council oversight and a new reporting structure. And though almost everyone expects the city would continue employing armed police officers, there would no longer be a required minimum staffing level. The ballot language says the new Department of Public Safety “could include licensed peace officers (police officers), if necessary.”Supporters of the measure, which would amend the City Charter, have largely steered away from the “defund” language, and there is little agreement on what the amendment might mean in practice. Some see it is a first step toward the eventual abolition of the police, or a way to shrink the role of armed officers to a small subset of emergencies.But other supporters of the amendment, including Kate Knuth, a mayoral candidate, say they would actually add more officers to a new Public Safety Department to make up for large numbers who have resigned or gone on leave since Mr. Floyd’s murder.Kate Knuth, a mayoral candidate and former state lawmaker, supports the amendment and says the number of officers would go up if it passes.Jenn Ackerman for The New York Times“It’s clear people want to trust that we have enough officers to do the work we need them to do,” Ms. Knuth, a former state lawmaker, said. “But the goal is public safety. Not a specific number of police.”Concerns about police misconduct persist in Minneapolis: This year, the city has fielded more than 200 complaints.But worries about crime also are shaping much of the conversation, and even as Minneapolis voters weigh replacing the department, city officials have proposed increasing the police budget by $27.6 million, or 17 percent, essentially restoring earlier cuts. At least 78 people have been killed in the city this year, and 83 people were killed last year, the most since the 1990s.“Minneapolis is in a war zone — this is a war going on where your kids are not safe,” said Sharrie Jennings, whose 10-year-old grandson was shot and severely wounded in April while being dropped off at a family member’s house. “We need more police.”For his part, the police chief, Medaria Arradondo, has urged voters to reject the amendment, saying it fails to provide a clear sense of what public safety would really look like if the Police Department were to vanish.“I was not expecting some sort of robust, detailed, word-for-word plan,” Chief Arradondo said in a news conference this week. “But at this point quite frankly I would take a drawing on a napkin.”Some Black leaders have cast the amendment as the work of well-intentioned but misguided progressive white residents whose views are shaped by the relatively safe neighborhoods where they live. About 60 percent of Minneapolis residents are white.AJ Awed, a mayoral candidate, said he resented seeing white residents angered by the death of Mr. Floyd rushing to get rid of the Police Department.Caroline Yang for The New York TimesAJ Awed, another of Mr. Frey’s challengers, said he agreed that policing in Minneapolis needed to be overhauled and that the current system was prejudiced against Black residents. But he said he resented seeing white residents angered by the death of Mr. Floyd rushing to get rid of the Police Department, describing that as “cover because you feel guilty because of what you saw.”“We are very much sensitive to the delegitimization of our security apparatus,” said Mr. Awed, who is part of the city’s large Somali American community, and whose family sought refuge in the United States after a breakdown of public safety. “Policing is a fundamental structure in society.”Not everyone sees it that way.Minneapolis remains deeply shaken by what happened over the past 18 months: The video of Officer Derek Chauvin kneeling on Mr. Floyd’s neck. The looting and arson and police crackdown that followed. The months of boarded windows and helicopters flying overhead. Then the trial this year of Mr. Chauvin, who was convicted of murder.For some, trust in law enforcement has been frayed beyond repair.Demetria Jones, 18, a student at North Community High School, said she planned to vote for the amendment and had become more wary of officers since Mr. Floyd’s death.“I didn’t realize how much they didn’t care about us and didn’t care about our lives until I watched that video,” Ms. Jones said.Among Black residents, who make up about 19 percent of the population, the amendment fight has laid bare a generational divide. Many older leaders, some veterans of the civil rights era, are opposed, while younger activists were largely responsible for the campaign that collected signatures to put the amendment to a vote.Nekima Levy Armstrong, a civil rights lawyer and the former head of the Minneapolis chapter of the N.A.A.C.P., opposes the amendment, saying the language is too vague.The police station for the Third Precinct was burned during unrest.Aaron Nesheim for The New York Times“When you think about the history of policing in the city of Minneapolis and how hard so many of us have fought over the years to bring awareness, to push for policy changes,” Ms. Levy Armstrong said, “it doesn’t make sense to me at this point that there is not a written plan.”One evening last week, Matthew Thompson, 33, stood holding his baby in Farwell Park in North Minneapolis. He had been an early supporter of proposals to defund the police and had fully expected to vote for the amendment. But when he recently dropped his young son at day care, he learned that the car windows of one of the employees had been shattered by a stray bullet, and he had been hearing more gunshots at night, he said.All of it left him uncertain about how he will vote on Tuesday. “I’m still really conflicted on this,” he said. More