It's long been clear that Presidents can be impeached for "high crimes and misdemeanors" that are not actual violations of federal criminal law. In an oft-cited passage from Federalist No.65, Alexander Hamilton wrote that impeachable offenses "are of a nature which may with peculiar propriety be denominated
political as they related chiefly to injuries done immediately to the society itself." The involve "the misconduct of public men, or, in other words, from the abuse or violation of some public trust." This, at the moment, is the core of the case against
Donald Trump for his interactions with the President of Ukraine -- that he abused his power by using taxpayer dollars as a tool to extract information potentially damaging to a political rival.
Jeffery Toobin - The New Yorker
In His Dealings with Ukraine, Did Donald Trump Commit a Crime? | The New Yorker