It is not a good idea to have a paid staff member serve on the board and may even be limited by your state’s nonprofit laws. The chief reasons staff members do not usually sit on a nonprofit’s board is the risk of a conflict of interest and board inurement.
Executive Directors are hired, fired, and supervised by the board, so being a voting member of the board would obviously be a conflict of interest. However, the board needs the ED’s presence at board meetings to keep it informed and educated about what the organization is doing. In volunteer-only organizations, those volunteers might do the work, and some may serve on the board.
Foundations providing grants also often restrict paid Executive Directors from serving on the board.
Unpaid Executive Directors should refrain from serving on the board as well. In addition to the conflict of interest on voting on their salary votes on duties can also be problematic. Also, a goal of most nonprofit organizations is to have the Executive Director be a paid staff position.
In my practice I have had the IRS refuse to approve a 501c3 Tax Exempt application for a nonprofit who had paid staff on the board. This shows that the IRS cares about whether a new nonprofit has a paid Executive Director on the board.
Sometimes state laws permit staff to serve on nonprofit boards, with California being the prime example.