Board of supervisors

Capitalize "board of supervisors" when it is used as part of the proper name of a government organization. E.g.: "... the Orange County Board of Supervisors voted Wednesday ..."

As with the term "city council," capitalize "board of supervisors" when referring to the same board but dropping "Orange County." E.g.: "The Board of Supervisors will meet in Santa Ana on Friday."

Lowercase in generic uses. E.g.: "A board of supervisors can be essential for any county's government."

Lowercase "board" when it stands alone.

For more, see the AP style guide entry on "city council."