Mr. Chertoff, a former federal judge and prosecutor, said that profiling techniques not relating to ethnicity were already available to the authorities, and that ethnic profiling was counterproductive.

“Not only is it a waste of time, but you’re offending people who in many ways you want to be your allies,” he said, adding, “When you ethnically profile, you play into the hands of the enemy.”

If elected, Mr. Trump would have little direct power over local law enforcement, but presidents do set the tone at the Justice Department, which can sue municipalities that violate civil rights. Under President Obama, the Justice Department has sought to address racial unrest by scrutinizing police departments in cities like Baltimore and Cleveland. Mr. Trump has been critical of the Obama administration’s oversight of the police, raising the prospect that he would take a very different approach.

Presidents have far broader discretion in areas related to national security and immigration. In some instances, Mr. Trump has advocated unprecedented measures that would be unlikely to survive legal scrutiny, such as a proposal to ban all Muslim immigration that he offered during the Republican primaries.

Mr. Trump has also proposed to enlist local law enforcement agencies to fulfill his promise to deport millions of people who entered the country illegally, largely from Latin America and Asia. He has pledged to “expand and revitalize” a federal program known as 287(g), which empowers local police departments to help enforce federal immigration law.

But like New York’s stop-and-frisk policy, this program has come under fire for its racial impact. In 2012, the Obama administration discontinued its most hotly criticized element, which allowed the police to question people about their immigration status on the street, following concerns that it violated the rights of American citizens of Hispanic descent.

“In some places, local law enforcement wound up picking up people who were citizens or who had legal status in the country,” said David Martin, who served as principal deputy general counsel of the Department of Homeland Security from January 2009 to December 2010. “There has been no close attention at all on the part of the Trump campaign policy people to see what’s being done right now, what is effective and what are the trade-offs that the Obama administration is making.”