NEW YORK — New York City police and mental health clinicians who engage emotionally disturbed people on streets and subways will now be armed with a much broader interpretation of state law to institutionalize those who pose a risk to themselves or others. That broader, more defined legal reading will likely result in the city placing more mentally ill homeless people into hospitals against their will. Mayor Eric Adams announced Tuesday that he issued a new directive to city agencies clarifying the way first responders and other city workers should approach those exhibiting acute mental distre…