In the letter, written in November and released under the Official Information Act, English outlines his expectations for feedback on the Reserve Bank's performance.
He requests a regular, six-monthly meeting with the board and notes that "greater visibility of the board's activities throughout the year would also be welcome".
The letter makes reference to the performance of the Reserve Bank governor although it includes no specific comment on performance of current governor Graeme Wheeler.
"I would expect you to discuss your assessment of the governor's performance from time to time," English writes.
Wheeler has faced criticism from some economic commentators over the decision to lift interest rates in 2014, a move that has since been reversed to counter persistently low inflation.
However, in a February speech English noted that "central banks around the world were grappling with low inflation" and "New Zealand was better placed than most".
It is normal for the Finance Minister to send a letter of expectation directly to the governor, although the chairman was copied in for the first time in March last year, Treasury papers show.
The Bank's board secretary and head of communications Mike Hannah yesterday confirmed the board received its first letter of expectations from the minister late last year "following discussions initiated by the board".
"The board's role is described in high-level terms in the Reserve Bank Act," he said. "The letter of expectations provides more contemporary context, just as the minister's letter of expectations to the governor does each year."
The Bank will publish the minister's letter in June.
