CHARLOTTE, N.C. — The protests filling television screens since a police shooting here have added a volatile new element to the presidential race in North Carolina, where the candidates are locked in fierce competition.  It is too soon to know how this latest edition of the wrenching national debate over policing and race will play out in this battleground state, where nearly one in four voters are African-American.  But both nominees seized on the fatal shooting of a 43-year-old black man on Tuesday in ways meant to appeal to core supporters.  Hillary Clinton’s campaign said Thursday that three of the “mothers of the movement” — women whose children had died in confrontations with the police — would visit North Carolina next week to speak about Mrs. Clinton’s plans to reform criminal justice.  Donald J. Trump, her Republican rival, called on Thursday for a “national anti-crime agenda,” an echo of his law-and-order theme after earlier police shootings when he had generally belittled the Black Lives Matter movement.  “Many Americans are watching the unrest in Charlotte unfolding right before their eyes on the TV screens,” he said in a speech in Pittsburgh. “Others are witnessing the chaos and the violence firsthand.”  The traditional wisdom of political strategists is that images of civil mayhem like the smashed storefronts in Charlotte play miserably for Democrats, and that law-and-order calls have put steel in the spines of Republicans since the days of Richard M. Nixon.  But with polls in North Carolina showing a deadlocked race for president, with only 5 to 8 percent of voters undecided, it is not clear that even this powerful an event, leading the governor to declare a state of emergency, can persuade voters on the fence.  “Trump saying he’s for ‘law and order’ is a political slogan,” said Carter Wrenn, a longtime Republican strategist in the state. “It’s a fine slogan. Many swing voters will agree with it. But the swing voters dislike Trump, so it’s unlikely any political slogan will change their vote.”  He said undecided voters were looking for strong evidence to overcome their doubts about Mr. Trump’s judgment and temperament. “Does Trump have an idea that will work, as opposed to a slogan?” Mr. Wrenn asked.  Mr. Trump almost certainly needs to win North Carolina, along with Florida and Ohio, to be elected. Mrs. Clinton could lose the state, as President Obama did in 2012, and find other routes through the Electoral College to capture the White House. But she is fighting hard, with an extensive ground game and hefty advertising budget.  Although Mr. Obama lost here four years ago, his victory in the state in 2008 announced North Carolina’s evolution from a solidly Republican state into a presidential battleground, the result of changing demographics. Newcomers from the North, drawn to banking jobs in Charlotte and to the high-tech Raleigh-Durham region, tugged the state from its conservative moorings.  Its competitiveness is reflected this year in three tight statewide races — for the governorship, the Senate and the presidency.  Gov. Pat McCrory and Senator Richard M. Burr, both Republicans, are facing a backlash against conservative measures enacted in the state since Republicans took full control in the capital, Raleigh, in 2012. The so-called bathroom bill, HB-2, put restrictions on transgender rights, leading corporations and sports leagues to cancel job-generating plans for the state.  “That issue is reaching a whole audience that is pretty checked out from politics,” said Michael Halle, Mrs. Clinton’s director of strategy and analytics in the battleground states.  The unpopularity of HB-2 may have a “reverse-coattail effect” on the presidential race, said Jason Husser, a political scientist and pollster at Elon University, generating a bit of added support for Mrs. Clinton by mobilizing progressive voters to turn out.  But Democrats’ hopes for revenge on Mr. McCrory have been shattered before, most recently in 2014, when they counted on a backlash against the conservative governor and the Republican Legislature, only to see Thom Tillis, the speaker of the State House of Representatives, ascend to the United States Senate.  Historically, Democrats held power in Raleigh for so long that Republicans are still seen as the insurgent party, benefiting Mr. Trump, said Mac McCorkle, a former Democratic strategist now on the faculty of Duke University.  Mr. Trump has visited the state often, including on Tuesday, just before the shooting of Keith L. Scott, which was followed by violent demonstrations that included a shooting Wednesday night. He repeated a refrain meant to appeal to black voters — “What do you have to lose?” — but he has almost no support here among African-Americans. A recent Elon poll showed that he was the choice of just 2 percent of likely black voters in North Carolina.  Newt Gingrich, a surrogate of Mr. Trump’s, went further on Wednesday night, predicting on Fox News, amid scenes of Charlotte unrest, that Mr. Trump might do “surprisingly well in the inner cities” because of the mayhem.  Courtney A. Crowder, a senior adviser to the Obama campaign in the state in 2012, dismissed that notion. “I can’t even follow the logic,” said Mr. Crowder, who is working for an independent group this year to raise black turnout.  The question of whether African-Americans will turn out without Mr. Obama on the ballot hangs over the Clinton campaign. Black voters cast 23 percent of ballots in North Carolina in the past two presidential elections. It was Mr. Obama’s erosion among whites that accounted for his loss four years ago after he won North Carolina in 2008.  Mr. Crowder said he saw no decline in the intent of blacks to vote. Partly, he said, that is because of anger at the state’s Republican-led effort to restrict voting access in a sweeping law in 2013. A federal appeals court struck down the law in July, ruling that it was intentionally discriminatory.  “You have people who have a tough time recognizing their North Carolina,” Mr. Crowder said.
Hillary Clinton and Donald J. Trump seized on the shooting and protests in Charlotte, but it was unclear whether they could sway undecided voters.