WASHINGTON—The Boston Federal Reserve will not release documents that could show whether its former president vetted a series of personal investments last year with its ethics officer, a spokesman for the regional Fed bank said, a key point in an ongoing ethics controversy at the U.S. central bank. Eric Rosengren, along with Dallas Fed President Robert Kaplan, stepped down after details of their trading activities in 2020 were reported in the media last month, raising questions about whether Fed rules on policymakers’ financial investments are strict enough given their market-sensitive roles. Their investing activities and those of other top Fed officials including Chair Jerome Powell, in a year when the central bank delivered an unprecedented response to the economic threat posed by the coronavirus pandemic, have erupted into a full-blown controversy that may weigh on whether Powell is reappointed as Fed chief. In a statement issued shortly after the initial …