The New York Police Department violated the Constitution with its practice of stopping and searching people suspected of criminal activity, a federal judge ruled Monday in a decision likely to lead police departments across the country to take a close look at their crime-fighting tactics.

Finding that New York City's so-called stop-and-frisk program amounted to "indirect racial profiling" by targeting blacks and Hispanics disproportionate to their populations, U.S. District Judge Shira Scheindlin ordered the installation...