For the second time in a decade, a new mayor of New York City is being tested by the killing of two police officers. In 2014, less than a year into Bill de Blasio’s first term, a Baltimore man who brought a gun to town shot two cops dead, in Brooklyn. The man had posted on social media about avenging the police killings of Eric Garner and Michael Brown. De Blasio had come into office vowing to put an end to racist policing practices at the N.Y.P.D. Many cops held him responsible for their colleagues’ deaths. At a funeral for one of them, officers in uniform turned their backs on the mayor. “There’s blood on many hands,” Patrick Lynch, the head of the city’s largest officers’ union, said. “That blood on the hands starts on the steps of City Hall, in the office of the mayor.”